Solving TwoStep Equations M 08 BE 3 1

Solving Two-Step Equations M 08. B-E. 3. 1. 2 SOLVE LINEAR EQUATIONS THAT HAVE RATIONAL NUMBER COEFFICIENTS, INCLUDING EQUATIONS WHOSE SOLUTIONS REQUIRE EXPANDING EXPRESSIONS USING THE DISTRIBUTIVE PROPERTY AND COLLECTING LIKE TERMS.

Solve Two-Step Equations Objective: Students will be able to solve two-step equations showing their steps. Solve 2 -step equations using a combination of the four operations: o. Addition o. Subtraction o. Multiplication o. Division

Use two steps to solve equations This is an equation where you will need more than one step to solve the equation. How can you tell? 2 x – 5 = 17

Use two steps to solve equations This is an equation where you will need more than one step to solve the equation. How can you tell? 2 x – 5 = 17 There is more than one operation in the equation: multiplication and subtraction.

Use two steps to solve equations 2 x – 5 = 17 Our first task is to isolate the term with the variable. So, that means we want 2 x by itself. How do we do that?

Use two steps to solve equations We need to add 5 to both sides of the equation. 2 x – 5 = 17 + 5 +5 (add the number that is subtracted from the variable) 2 x = 22

Use two steps to solve equations Now we have this simple equation. You know what to do! 2 x = 22 2 2 x = 11 Check the solution.

Use two steps to solve equations Check the solution. Start with the original equation. 2 x – 5 = 17 Substitute the solution in for the variable. Check: 2(11) – 5 = 17

Use two steps to solve equations Continue checking using order of operations. 2(11) – 5 = 17 22 – 5 = 17 This shows the answer is correct!

Use two steps to solve equations Try one on your own. 5 y + 7 = -28 original equation What do you do first? Type your answer in the chat.

Use two steps to solve equations 5 y + 7 = -28 First, subtract 7 from both sides of the equation. (You want to isolate the 5 y. ) 5 y + 7 = -28 – 7 5 y = -35 What happens now?

Use two steps to solve equations What now? To isolate the y, divide both sides by 5. 5 y = -35 5 5 y = -7 Now check the solution!

Use two steps to solve equations Start with the original equation and substitute the solution in for the variable. Simplify. 5 y + 7 = -28 5(-7) + 7 = -28 -35 + 7 = -28 The solution is correct!

Use two steps to solve equations

Review solving two-step equations

Review solving two-step equations Answers. 1. 3 x – 5 = 19 + 5 3 x = 24 3 3 x = 8 Check: *3 x – 5 = 19 3 ● 8 – 5 = 19 24 – 5 = 19 = 19 � correct

Are you showing your steps? All steps must be shown.

Review solving two-step equations

Review solving two-step equations Answers. 4. 8 + 4 f = -16 – 8 4 f = -24 4 4 f = -6 * 8 + 4 f = -16 8 + 4(-6) = -16 8 + -24 = -16 � It is correct!

Review solving two-step equations Answers. 5. 7 + 5 n = 37 – 7 5 n = 30 5 5 n=6 * 7 + 5 n = 37 7 + 5 ● 6 = 37 7 + 30 = 37 37= 37 �

Review solving two-step equations Answers.

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Warm-up: simplify these expressions. Add or subtract. 1. ) 14 – (-10) = 2. ) -23 – 30 = 3. ) -6 – (-8) = 4. ) 9 – (-11) =

Let’s solve this equation. What do we need to do first? 2 x – (-7) = -13

Solving tricky two-step equations Sometimes there are other pieces of information we need to consider when solving equations. Example 1: How do we start this problem? -6 + 4 y = 18

Solving tricky two-step equations Example 1: How do we start this problem? -6 + 4 y = 18 What do you think? (We know we want to isolate the 4 y. )

Solving tricky two-step equations Example 1: How do we start this problem? -6 + 4 y = 18 We need to add 6 to both sides of the equation. It looks like we should start by subtracting, but the 6 is negative. So to eliminate it we need to add 6. (You could subtract -6, but that is the same as adding 6. )

Solving tricky two-step equations Solve example 1. -6 + 4 y = 18 +6 4 y = 24 4 4 y = 6 * -6 + 4 y = 18 -6 + 4(6) = 18 -6 + 24 = 18 18 = 18 �

Example 2

Solve and check these equations. Make sure you are showing all steps.

Solving tricky two-step equations Example 3: What should you do first? 7 – 3 g = 22 Write what you think in the chat. Your answer should include an operation and which term you are using.

Solving tricky two-step equations Example 3: What should you do first? 7 – 3 g = 22 o. You need to subtract 7 from both sides of the equation. (The 7 is not being subtracted from 3 g. ) o. Then, you need to be sure you keep the minus sign with the 3 g when you bring it down to the next step.

Solving tricky two-step equations Solve example 3: 7 – 3 g = 22 – 7 -3 g = 15 (Be sure you bring the sign with the 3 g. ) -3 -3 g = -5

Solving tricky two-step equations Check example 3: 7 – 3 g = 22 7 – 3(-5) = 22 7 – -15 = 22 7 + 15 = 22 � correct

Example 4 20 – 4 c = -68 (this is #14 from the face worksheet).

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Review solving tricky two-step equations

Review solving tricky two-step equations Answers. 1. 3 x – (-5) = 35 * 3 x – (-5) = 35 3 x + 5 = 35 3(10) – (-5) = 35 – 5 30 + 5 = 35 3 x = 30 35 = 35 � 3 3 x = 10

Review solving tricky two-step equations – answers

Review solving tricky two-step equations – answers 3. 12 = -3 m – 6 * 12 = -3 m – 6 +6 12 = -3(-6) – 6 18 = -3 m 12 = 18 – 6 -3 12 = 12 � -6 = m

Review solving tricky two-step equations – answers 4. 5 – 7 m = 54 – 5 -7 m = 49 -7 -7 m = -7 * 5 – 7 m = 54 5 – 7(-7) = 54 5 – -49 = 54 5 + 49 = 54 ��