PRE-ALGEBRA

PRE-ALGEBRA

Lesson 7-1 Warm-Up

PRE-ALGEBRA

What is a two-step equation?

How can you use a model to show how to solve a two-step equation?

two-step equation: an equation that involves “undoing” two operations

In the following model, represents -1, represents 1, and represents a varibable, like x. This means that equals 0 (in other words, they “cancel each other out”), since 1 – 1 = 0.

Solving Two-Step Equations (7-1)

PRE-ALGEBRA

To solve a two-step equation:

1.“undo” (work backwards) addition or subtraction (anything added or subtracted) on the variable side by doing the opposite operation to both sides of the equal sign, and

2.“undo” (work backwards) multiplication or division (anything attached to the variable) by doing the opposite operation to both sides of the equal sign.

Example: Solve 3n – 6 = 10

3n – 6 = 15 Given

+ 6 + 6 Undo -6 from the variable side by adding 6 to both sides. 3n = 21

= Undo times 3 from the variable side by dividing both sides by 3..

3n3

213

Solving Two-Step EquationsLESSON 7-1

Additional Examples

How do you solve a two-step equation?

n = 7 Simplify.

1

1

7

1

1

+ 0

PRE-ALGEBRA

Example: Lynn want to save $900 to go to Puerto Rico. She saves $45 each week and now has $180. How many more weeks will it take for Lynn to save $900.

Words: $180 plus $45 each week equals $900.Define: Let w = number of additional weeks Lynn needs to save forEquation: 180 + 45 • w = 900

180 + 45w = 900 Given

- 180 - 180 Undo +180 from the variable side by subtracting 180 from both sides. 45w = 720

= Undo times 45 from the variable side by dividing both sides by 45..

45n45

72045

Solving Two-Step EquationsLESSON 7-1

Additional Examples

w = 16 Simplify.

It will take Lynn 16 more weeks to save $900.

1

1 1

16

1

0 +

PRE-ALGEBRA

Solve 5v – 12 = 8.

5v – 12 = 8

+ 12 +12 Add 12 to each side.

5v = 20 Simplify.

v = 4 Simplify.

= Divide each side by 5.5v5

205

Check:  5v – 12 = 8

5(4) – 12 8 Replace v with 4.

20 – 12 8 Multiply.

8 = 8 Simplify.

Solving Two-Step EquationsLESSON 7-1

Additional Examples

+ 0

1

1

1

PRE-ALGEBRA

Solve 7 – 3b = 1.

7 – 3b = 1

–7 –7 Subtract 7 from each side.

-3b = -6 Simplify.

b = 2 Simplify.

= Divide each side by –3.–3b–3

–6–3

Solving Two-Step EquationsLESSON 7-1

Additional Examples

0 +1

1

1

PRE-ALGEBRA

You borrow $350 to buy a bicycle. You agree to

pay $100 the first week, and then $25 each week until

the balance is paid off. To find how many weeks w it

will take you to pay for the bicycle, solve 100 + 25w =

350.

It will take you 10 weeks to pay for the bicycle.

100 + 25w = 350

– 100 – 100   Subtract 100 from each side.

25w = 250 Simplify.

w = 10 Simplify.

= Divide each side by 25.25w25

25025

Solving Two-Step EquationsLESSON 7-1

Additional Examples

0 +1

1

1

PRE-ALGEBRA

Solve each equation.

1. 12x – 14 = 10 2. + 7 = –4

3. 9 – w = 13 4. –22 – = –15

5. 4d – 57 = 7

r3

q5

2 –33

–4 –35

16

Lesson Quiz

Solving Two-Step EquationsLESSON 7-1