Chapter 3 Lesson 5Solving 2-Step Equations

Pgs. 120-124

What you will learn:To solve 2-step equations!

Background

A two step equation contains two operations.In the equation 2x + 1 = 9, x is multiplied by 2and then 1 is added. To solve two-step equations,use inverse operations to undo each operation inreverse order. You can solve 2x + 1 = 9 in twosteps.

Step 1: First, undo addition2x + 1 = 9

2x + 1 -1 = 9 -1 Subtract 1 from each side 2x = 8

Step 2: Undo the multiplication2x = 82x = 8 2 2 x = 4

How do you do the check of 2x + 1 = 9 if x = 4?

Replace the x with 4 in the ORIGINALProblem and solve step by step.

2(4) + 1 = 9 8 + 1 = 9 9 = 9

This problem checks out!

Solve a two-step equation andcheck the solution.

5x - 2 = 13

Step 1: Undo the subtraction. 5x - 2 +2 = 13 +2

5x = 15

Step 2: Undo the multiplication 5x = 15

5x = 15 5 5 x = 3

Check: 5x - 2 = 13 5(3) - 2 = 13 15 - 2 = 13 13 = 13

Solve the equation and check the answer.

4 = n + 11 6

What do you do first? Undo the addition

4 - 11 = n + 11 -11 6

-7 = n 6

What do you do next? Undo the division

-7(6) = n (6) 6 -42 = n

Now check your answerIn the original problem.

4 = n + 11 64 = -42 + 11 6

4 = -7 + 11

4 = 4

Remember, in order for a check to work out, both sides of the equation needto equal the same!!

Solve an equation withNegative coefficients

4 - x = 10

Think of the problem as 4 - 1x = 10 4 - 4 - 1x = 10 - 4

-1x = 6

-1x = 6 -1 -1

x = -6

Check: 4 - x = 10 4 - (-6) = 10

10 = 10

Combine Like Terms beforesolving

m - 5m + 3 = 47 Remember it can be rewrittenas m + (-5m) + 3 = 47

Combine like terms: m - 5m + 3 = 47 -4m + 3 = 47

Subtract 3 from each side: -4m + 3 - 3 = 47 - 3Simplify: -4m = 44

Divide both sides by -4: -4m = 44 -4 -4

Simplify: m = -11Check: m - 5m + 3 = 47

-11 - 5(-11) + 3 = 47 -11 + 55 + 3 = 47

44 + 3 = 47 47 = 47

Use an equation to solve aproblem

A telephone calling card allows for 25¢ perminute plus a one-time service charge of 75¢. If thetotal cost of the card is $5, solve 25m + 75 = 500 to find the number of minutes you can use the card.

Step 1: Undo the addition 25m + 75 -75 = 500 -75

25m = 425

Step 2: Undo the multiplication25m = 425 25 25

m = 17

Check:25(17) + 75 = 500425 + 75 = 500 500 = 500

You try. Look at the questionsCarefully!

3y + 4 = 13

20 - z = 11

3n + n - 4 = 12

3y + 4 -4 = 13 - 43y = 93y = 9 y = 3 3 3

20 - 20 - z = 11 - 20-z = -9 -z = -9 -1 -1 z = 9

4n - 4 + 4 = 12 + 44n= 16 4n = 16 4 4 n = 4

Check:3(3) + 4 = 13 9 + 4 = 13 13 = 13

20 - 9 = 11 11 = 11

3(4) + 4 - 4 = 12 12 = 12