Algebra 1 Solving Equations Math is Hip Solutions

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prerequisite Skills Needed: - Order of Operations - Algebraic Properties Previous Video: Equations w/Variables on Both Sides

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ An important part of math is being able to justify your solutions. You gotta PROVE you know _____ what you’re doing! One way to do this is by understanding how solutions complete an equation. 4 x – 6 = x + 9 We earlier solved this equation

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ An important part of math is being able to justify your solutions. You gotta PROVE you know _____ what you’re doing! One way to do this is by understanding how solutions complete an equation. 4 x – 6 = x + 9 -1 x = -x 3 x – 6 = 9 +6= +6 3 x = 15 3 = 3 x=5 We earlier solved this equation and got x = 5 for the solution.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ An important part of math is being able to justify your solutions. You gotta PROVE you know _____ what you’re doing! One way to do this is by understanding how solutions complete an equation. 4 x – 6 = x + 9 4(5) – 6 = (5) + 9 We earlier solved this equation and got x = 5 for the solution. So we can now substitute 5 in place of x into the original equation to check and to prove that it was solved correctly.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ An important part of math is being able to justify your solutions. You gotta PROVE you know _____ what you’re doing! One way to do this is by understanding how solutions complete an equation. 4 x – 6 = x + 9 4(5) – 6 = (5) + 9 We earlier solved this equation and got x = 5 for the solution. So we can now substitute 5 in place of x into the original equation to check and to prove that it was solved correctly. Don’t Forget to follow Order of Operations (PEMDAS)!

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ An important part of math is being able to justify your solutions. You gotta PROVE you know _____ what you’re doing! One way to do this is by understanding how solutions complete an equation. 4 x – 6 = x + 9 4(5) – 6 = (5) + 9 20 - 6 = 5 + 9 Don’t Forget to follow Order of Operations (PEMDAS)! We earlier solved this equation and got x = 5 for the solution. So we can now substitute 5 in place of x into the original equation to check and to prove that it was solved correctly.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ An important part of math is being able to justify your solutions. You gotta PROVE you know _____ what you’re doing! One way to do this is by understanding how solutions complete an equation. 4 x – 6 = x + 9 4(5) – 6 = (5) + 9 20 - 6 = 5 + 9 14 = 14 We earlier solved this equation and got x = 5 for the solution. So we can now substitute 5 in place of x into the original equation to check and to prove that it was solved correctly. Because we ended up with a TRUE statement -(it is true that 14 equals 14)then we have PROVED that x = 5 for this equation! Great job!

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ An important part of math is being able to justify your solutions. You gotta PROVE you know _____ what you’re doing! One way to do this is by understanding how solutions complete an equation. 4 x – 6 = x + 9 4(5) – 6 = (5) + 9 20 - 6 = 5 + 9 14 = 14 It is ALWAYS a good idea to check your solutions! We earlier solved this equation and got x = 5 for the solution. So we can now substitute 5 in place of x into the original equation to check and to prove that it was solved correctly. Because we ended up with a TRUE statement -(it is true that 14 equals 14)then we have PROVED that x = 5 for this equation! Great job!

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ x=5 Here’s a way to see it visually as well: 4 x – 6 = x + 9 Remember to keep the sides balanced. x x -6 x 9

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ x=5 Here’s a way to see it visually as well: 4 x – 6 = x + 9 x x -6 x 9

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ x=5 Here’s a way to see it visually as well: . 4 x – 6 = x + 9 4(5) – 6 = (5) + 9 5 5 -6 5 9

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ x=5 Here’s a way to see it visually as well: . 4 x – 6 = x + 9 4(5) – 6 = (5) + 9 5 5 -6 20 - 6 = 5 + 9 5 9

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ x=5 Here’s a way to see it visually as well: . 4 x – 6 = x + 9 4(5) – 6 = (5) + 9 5 5 -6 20 - 6 = 5 + 9 14 = 14 5 9

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ You should also be able to state the Algebraic Properties that prove each step. _____ Prove that x = 5 when 4 x – 6 = x + 9. (What step did you take? ) Steps (How do you know you can do that? ) Reasons

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ You should also be able to state the Algebraic Properties that prove each step. _____ Prove that x = 5 when 4 x – 6 = x + 9. (What step did you take? ) Steps (How do you know you can do that? ) Reasons Many students get stuck on this, but don’t let it fluster you!

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ You should also be able to state the Algebraic Properties that prove each step. _____ Prove that x = 5 when 4 x – 6 = x + 9. (What step did you take? ) Steps Many students get stuck on this, but don’t let it fluster you! (How do you know you can do that? ) Reasons Break each step down and state the rule that allows you to perform that math operation.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ You should also be able to state the Algebraic Properties that prove each step. _____ Prove that x = 5 when 4 x – 6 = x + 9. (What step did you take? ) Steps Many students get stuck on this, but don’t let it fluster you! (How do you know you can do that? ) Reasons Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ You should also be able to state the Algebraic Properties that prove each step. _____ Prove that x = 5 when 4 x – 6 = x + 9. (What step did you take? ) Many students get stuck on this, but don’t let it fluster you! (How do you know you can do that? ) Steps Reasons 4 x – 6 = x + 9 Given information Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ You should also be able to state the Algebraic Properties that prove each step. _____ Prove that x = 5 when 4 x – 6 = x + 9. (What step did you take? ) Steps 4 x – 6 = x + 9 -1 x =-1 x 3 x – 6 = 9 Many students get stuck on this, but don’t let it fluster you! (How do you know you can do that? ) Reasons Given information Break each step down and state the rule that allows you to perform that math operation. Pretend you are a “math lawyer” proving your case!

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ You should also be able to state the Algebraic Properties that prove each step. _____ Prove that x = 5 when 4 x – 6 = x + 9. (What step did you take? ) Steps 4 x – 6 = x + 9 -1 x =-1 x 3 x – 6 = 9 Many students get stuck on this, but don’t let it fluster you! (How do you know you can do that? ) Reasons Given information Break each step down and state the rule that allows you to perform that math operation. Subtraction Prop. of Equality Pretend you are a “math lawyer” proving your case!

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ You should also be able to state the Algebraic Properties that prove each step. _____ Prove that x = 5 when 4 x – 6 = x + 9. (What step did you take? ) Steps 4 x – 6 = x + 9 -1 x =-1 x 3 x – 6 = 9 +6= + = 15 63 x Many students get stuck on this, but don’t let it fluster you! (How do you know you can do that? ) Reasons Given information Break each step down and state the rule that allows you to perform that math operation. Subtraction Prop. of Equality Pretend you are a “math lawyer” proving your case!

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ You should also be able to state the Algebraic Properties that prove each step. _____ Prove that x = 5 when 4 x – 6 = x + 9. (What step did you take? ) Steps 4 x – 6 = x + 9 -1 x =-1 x 3 x – 6 = 9 +6= + = 15 63 x Many students get stuck on this, but don’t let it fluster you! (How do you know you can do that? ) Reasons Given information Break each step down and state the rule that allows you to perform that math operation. Subtraction Prop. of Equality Addition Prop. of Equality Pretend you are a “math lawyer” proving your case!

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ You should also be able to state the Algebraic Properties that prove each step. _____ Prove that x = 5 when 4 x – 6 = x + 9. (What step did you take? ) Steps 4 x – 6 = x + 9 -1 x =-1 x 3 x – 6 = 9 +6= + = 15 63 x 3 = 3 Many students get stuck on this, but don’t let it fluster you! (How do you know you can do that? ) Reasons Given information Break each step down and state the rule that allows you to perform that math operation. Subtraction Prop. of Equality Addition Prop. of Equality Pretend you are a “math lawyer” proving your case!

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ You should also be able to state the Algebraic Properties that prove each step. _____ Prove that x = 5 when 4 x – 6 = x + 9. (What step did you take? ) Steps 4 x – 6 = x + 9 -1 x =-1 x 3 x – 6 = 9 +6= + = 15 63 x 3 = 3 Many students get stuck on this, but don’t let it fluster you! (How do you know you can do that? ) Reasons Given information Break each step down and state the rule that allows you to perform that math operation. Subtraction Prop. of Equality Addition Prop. of Equality Division Prop. of Equality Pretend you are a “math lawyer” proving your case!

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ You should also be able to state the Algebraic Properties that prove each step. _____ Prove that x = 5 when 4 x – 6 = x + 9. (What step did you take? ) Steps 4 x – 6 = x + 9 -1 x =-1 x 3 x – 6 = 9 +6= + = 15 63 x 3 = 3 x=5 Many students get stuck on this, but don’t let it fluster you! (How do you know you can do that? ) Reasons Given information Break each step down and state the rule that allows you to perform that math operation. Subtraction Prop. of Equality Addition Prop. of Equality Division Prop. of Equality Pretend you are a “math lawyer” proving your case!

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps (How do you know you can do that? ) Reasons For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps 3(x + 2) = - 5 – 2(x - 3) (How do you know you can do that? ) Reasons Given information For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps 3(x + 2) = - 5 – 2(x - 3) 3 x + 6 = - 5 – 2 x + 6 (How do you know you can do that? ) Reasons Given information For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps 3(x + 2) = - 5 – 2(x - 3) 3 x + 6 = - 5 – 2 x + 6 (How do you know you can do that? ) Reasons Given information Distributive Property For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps 3(x + 2) = - 5 – 2(x - 3) 3 x + 6 = - 5 – 2 x + 6 3 x + 6 = – 2 x + 6 + (-5) (How do you know you can do that? ) Reasons Given information Distributive Property For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps 3(x + 2) = - 5 – 2(x - 3) 3 x + 6 = - 5 – 2 x + 6 3 x + 6 = – 2 x + 6 + (-5) (How do you know you can do that? ) Reasons Given information Distributive Property Commutative Prop. Of Addition For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps 3(x + 2) = - 5 – 2(x - 3) 3 x + 6 = - 5 – 2 x + 6 3 x + 6 = – 2 x + 6 + (-5) 3 x + 6 = – 2 x + 1 (How do you know you can do that? ) Reasons Given information Distributive Property Commutative Prop. Of Addition For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps (How do you know you can do that? ) Reasons 3(x + 2) = - 5 – 2(x - 3) 3 x + 6 = - 5 – 2 x + 6 3 x + 6 = – 2 x + 6 + (-5) Commutative Prop. Of Addition 3 x + 6 = – 2 x + 1 Addition Given information Distributive Property For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps 3(x + 2) = - 5 – 2(x - 3) 3 x + 6 = - 5 – 2 x + 6 3 x + 6 = – 2 x + 6 + (-5) 3 x + 6 = – 2 x + 1 +2 x = +2 x 5 x + 6 = +1 (How do you know you can do that? ) Reasons Given information Distributive Property Commutative Prop. Of Addition For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps 3(x + 2) = - 5 – 2(x - 3) 3 x + 6 = - 5 – 2 x + 6 3 x + 6 = – 2 x + 6 + (-5) 3 x + 6 = – 2 x + 1 +2 x = +2 x 5 x + 6 = +1 (How do you know you can do that? ) Reasons Given information Distributive Property Commutative Prop. Of Addition Prop. of Equality For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps 3(x + 2) = - 5 – 2(x - 3) 3 x + 6 = - 5 – 2 x + 6 3 x + 6 = – 2 x + 6 + (-5) 3 x + 6 +2 x 5 x + 6 -6 5 x = – 2 x + 1 = +2 x = +1 = -6 = -5 (How do you know you can do that? ) Reasons Given information Distributive Property Commutative Prop. Of Addition Prop. of Equality For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps 3(x + 2) = - 5 – 2(x - 3) 3 x + 6 = - 5 – 2 x + 6 3 x + 6 = – 2 x + 6 + (-5) 3 x + 6 +2 x 5 x + 6 -6 5 x = – 2 x + 1 = +2 x = +1 = -6 = -5 (How do you know you can do that? ) Reasons Given information Distributive Property Commutative Prop. Of Addition Prop. of Equality Subtraction Prop. of Equality For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps 3(x + 2) = - 5 – 2(x - 3) 3 x + 6 = - 5 – 2 x + 6 3 x + 6 = – 2 x + 6 + (-5) 3 x + 6 +2 x 5 x + 6 -6 5 x 5 = – 2 x + 1 = +2 x = +1 = -6 = -5 = 5 (How do you know you can do that? ) Reasons Given information Distributive Property Commutative Prop. Of Addition Prop. of Equality Subtraction Prop. of Equality For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps 3(x + 2) = - 5 – 2(x - 3) 3 x + 6 = - 5 – 2 x + 6 3 x + 6 = – 2 x + 6 + (-5) 3 x + 6 +2 x 5 x + 6 -6 5 x 5 = – 2 x + 1 = +2 x = +1 = -6 = -5 = 5 (How do you know you can do that? ) Reasons Given information Distributive Property Commutative Prop. Of Addition Prop. of Equality Subtraction Prop. of Equality Division Prop. of Equality For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps 3(x + 2) = - 5 – 2(x - 3) 3 x + 6 = - 5 – 2 x + 6 3 x + 6 = – 2 x + 6 + (-5) 3 x + 6 +2 x 5 x + 6 -6 5 x 5 = – 2 x + 1 = +2 x = +1 = -6 = -5 = 5 x=-1 (How do you know you can do that? ) Reasons Given information Distributive Property Commutative Prop. Of Addition Prop. of Equality Subtraction Prop. of Equality Division Prop. of Equality For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course.

Algebra 1 – Solving Equations - Math is Hip™ Solutions and Justifying Your Work __________________________ Prove: If 3(x + 2) = -5 – 2(x - 3), then x = -1. _____ (What step did you take? ) Steps 3(x + 2) = - 5 – 2(x - 3) 3 x + 6 = - 5 – 2 x + 6 3 x + 6 = – 2 x + 6 - 5 3 x + 6 +2 x 5 x + 6 -6 5 x 5 = – 2 x + 1 = +2 x = +1 = -6 = -5 = 5 x=-1 (How do you know you can do that? ) Reasons Given information Distributive Property Commutative Prop. Of Addition Prop. of Equality For a handy guide to help you remember the Algebraic Properties, please see the handout in the resources/ extras section of this online course. NOW WHAT? 1) Re-watch/Re-wind 2) Master Practice Problems Subtraction Prop. of Equality 3) Next Skill: Translating Words Into Expressions & Equations Division Prop. of Equality

Algebra 1 – Solving Equations - Math is Hip™ Solving Equations w/Variables on Both __________________________ Here are some more examples – this time without Sides _____ the use of the balance scale. 1) Seek to Isolate the variable TO ONE SIDE. Be sure to practice, 2) Cancel by doing the opposite operation. practice equations before 3) Do the same thing to solving both sides. moving on to the next video! -1(y + 7) = - 6 y + 8 -y – 7 = - 6 y + 8 +6 y = + 6 y 5 y - 7 = +7 = 5 y = 5 y=5 2 8 1 +7 15 5 3 2(2 a + 1) = 3(a-2) • 3 1 1 2(2 a + 1)= 9(a-2) 4 a +WHAT? 2 = 9 a NOW +18 = 1)18 Re-watch/Re-wind 4 a + +18 20 = 9 a 2) Master=Practice Problems -4 a = 5 a. Solutions and 3) Next 20 Skill: 5 You 5 Work Checking 4=a