# Solving Equations with Solving Equations Variables on Both

Solving Equations with Solving Equations Variables on Both Sides Warm Up Lesson Presentation Lesson Quiz Holt. Algebra Mc. Dougal 1 Algebra 11 Mc. Dougal

Solving Equations with Variables on Both Sides Warm Up Simplify. 1. 4 x – 10 x – 6 x 2. – 7(x – 3) – 7 x + 21 3. 2 x + 3 4. 15 – (x – 2) 17 – x Solve. 5. 3 x + 2 = 8 2 6. 28 Holt Mc. Dougal Algebra 1

Solving Equations with Variables on Both Sides Homework Check: Kuta WS 1) 3) 5) 7) 9) 11) a=16 x=0 r = 20 v =15 x=9 v = -16 Holt Mc. Dougal Algebra 1 13) m = 5 15) n = 3 17) n = 11 21) n = 0 23) b = 12

Solving Equations with Variables on Both Sides Notebook Organization • Notebook/Graph paper in front • Dividers (in this order): – Warm-Up/Closings – Notes – Classwork – Homework – Quiz/Test Review – EOCT Review Holt Mc. Dougal Algebra 1

Solving Equations with Variables on Both Sides Objective Solve equations in one variable that contain variable terms on both sides. Holt Mc. Dougal Algebra 1

Solving Equations with Variables on Both Sides To solve an equation with variables on both sides, use inverse operations to "collect" variable terms on one side of the equation. Helpful Hint Equations are often easier to solve when the variable has a positive coefficient. Keep this in mind when deciding on which side to "collect" variable terms. Holt Mc. Dougal Algebra 1

Solving Equations with Variables on Both Sides Example 1: Solving Equations with Variables on Both Sides Solve 7 n – 2 = 5 n + 6 – 5 n 2 n – 2 = +2 2 n = To collect the variable terms on one side, subtract 5 n from both sides. 6 +2 8 Since n is multiplied by 2, divide both sides by 2 to undo the multiplication. n=4 Holt Mc. Dougal Algebra 1

Solving Equations with Variables on Both Sides Check It Out! Example 1 a Solve 4 b + 2 = 3 b – 3 b b+2= 0 – 2 b = – 2 Holt Mc. Dougal Algebra 1 To collect the variable terms on one side, subtract 3 b from both sides.

Solving Equations with Variables on Both Sides Whiteboard Problem Solve for x. 7 x + 2 = 5 x + 8 3 Holt Mc. Dougal Algebra 1

Solving Equations with Variables on Both Sides To solve more complicated equations, you may need to first simplify by using the Distributive Property or combining like terms. Holt Mc. Dougal Algebra 1

Solving Equations with Variables on Both Sides Example 2: Simplifying Each Side Before Solving Equations Solve 4 – 6 a + 4 a = – 1 – 5(7 – 2 a) Distribute – 5 to the expression in parentheses. 4 – 6 a + 4 a = – 1 – 5(7) – 5(– 2 a) 4 – 6 a + 4 a = – 1 – 35 + 10 a 4 – 2 a = – 36 + 10 a +36 40 – 2 a = + 2 a 40 = Holt Mc. Dougal Algebra 1 10 a +2 a 12 a Combine like terms. Since – 36 is added to 10 a, add 36 to both sides. To collect the variable terms on one side, add 2 a to both sides.

Solving Equations with Variables on Both Sides Example 2 Continued Solve 4 – 6 a + 4 a = – 1 – 5(7 – 2 a). 40 = 12 a Since a is multiplied by 12, divide both sides by 12. Holt Mc. Dougal Algebra 1

Solving Equations with Variables on Both Sides Check It Out! Example 2 b Solve 3 x + 15 – 9 = 2(x + 2) Distribute 2 to the expression in parentheses. 3 x + 15 – 9 = 2(x) + 2(2) 3 x + 15 – 9 = 2 x + 4 3 x + 6 = 2 x + 4 – 2 x x+6= – 6 x = – 2 Holt Mc. Dougal Algebra 1 4 – 6 Combine like terms. To collect the variable terms on one side, subtract 2 x from both sides. Since 6 is added to x, subtract 6 from both sides to undo the addition.

Solving Equations with Variables on Both Sides Whiteboard Problem Solve for x. 4(2 x – 5) = 5 x + 4 8 Holt Mc. Dougal Algebra 1

Solving Equations with Variables on Both Sides Whiteboard Problem Solve for a. 6 – 7(a + 1) = – 3(2 – a) Holt Mc. Dougal Algebra 1

Solving Equations with Variables on Both Sides Classwork: • You will complete 4 problems. STOP! at a time. You must have your work checked before you may proceed. • The problems you do not complete will be your homework for today. Closing: Our first quiz will be on Friday. What will you do to prepare for it? Holt Mc. Dougal Algebra 1

- Slides: 16