Chapter 7 Lesson 1Solving Equations with Variables on

Each Sidepgs. 330-333

Chapter 7 Lesson 1Solving Equations with Variables on

Each Sidepgs. 330-333

What you will learn:Solve equations with variables on

each side

What you will learn:Solve equations with variables on

each side

To solve equations with variables on each side, use the Addition or Subtraction Property of Equality to write an equivalent equation with the variables on

one side. Then solve the equation.

To solve equations with variables on each side, use the Addition or Subtraction Property of Equality to write an equivalent equation with the variables on

one side. Then solve the equation.

Quick Review: Chapter 3-3 (pg. 110-111)Subtraction Property of Equality: If you subtract the same number

from each side of an equation, the two sides remain equal. Ex.) x + 2 = 3

x + 2 – 2 = 3 – 2x = 1

Addition Property of Equality: If you add the same number to each side of an equation, the two sides remain equal.

Ex.) x – 2 = 5 x – 2 + 2 = 5 + 2 x = 7

Quick Review: Chapter 3-3 (pg. 110-111)Subtraction Property of Equality: If you subtract the same number

from each side of an equation, the two sides remain equal. Ex.) x + 2 = 3

x + 2 – 2 = 3 – 2x = 1

Addition Property of Equality: If you add the same number to each side of an equation, the two sides remain equal.

Ex.) x – 2 = 5 x – 2 + 2 = 5 + 2 x = 7

Example 1: Equations with Variables on Each Side

Example 1: Equations with Variables on Each Side

Remember, the goal is to isolate the variable by itself!

Solve 4x – 8 = 5x Step 1: Rewrite the problem 4x – 8 = 5xStep 2: Subtract 4x from each side to isolate the variable 4x – 8 = 5x Remember, what you do -4x = -4x one side of the equation, - 8 = x you must also do to the

other side!!!

Remember, the goal is to isolate the variable by itself!

Solve 4x – 8 = 5x Step 1: Rewrite the problem 4x – 8 = 5xStep 2: Subtract 4x from each side to isolate the variable 4x – 8 = 5x Remember, what you do -4x = -4x one side of the equation, - 8 = x you must also do to the

other side!!!

Now check: Substitute -8 everywhere there is an x. 4(-8) – 8 = 5(-8)

-32 – 8 = -40 -32 + (-8) = -40 -40 = -40

Example 2: Equations with Variables on Each Side

Example 2: Equations with Variables on Each Side

Solve 4k + 24 = 6k - 10

First, choose the side to isolate the variable on, hint: when isolating the variable, try to keep it positive.

Solve 4k + 24 = 6k - 10

First, choose the side to isolate the variable on, hint: when isolating the variable, try to keep it positive.

4k + 24 = 6k – 104k + 24 = 6k – 10

4k + 24 = 6k – 10 - 4k -4k Start by subtracting 4k from each

side

24 = 2k – 10 New equation (look familiar?)

+10 + 10 Add 10 to both sides

34 = 2k New equation (look familiar?)

2 2 17 = k Solve

4k + 24 = 6k – 10 - 4k -4k Start by subtracting 4k from each

side

24 = 2k – 10 New equation (look familiar?)

+10 + 10 Add 10 to both sides

34 = 2k New equation (look familiar?)

2 2 17 = k Solve

Now check: 4(17) + 24 = 6(17) – 10 68 + 24 = 102 – 10 92 = 92

Solve: 3.1w + 5 = 0.8 + wSolve: 3.1w + 5 = 0.8 + w

3.1w + 5 = 0.8 + w

- 1.0w - w 2.1w + 5 = 0.8 - 5 - 5.0 2.1w = -4.2 2.1 2.1 w = -2

3.1w + 5 = 0.8 + w

- 1.0w - w 2.1w + 5 = 0.8 - 5 - 5.0 2.1w = -4.2 2.1 2.1 w = -2

Check:3.1(-2) + 5 = 0.8 + (-2)-6.2 + 5 = -1.2 -1.2 = -1.2

Example 3: Use an Equation to Solve a Problem

Example 3: Use an Equation to Solve a Problem

Define a variable and write an equation to find each number. Then solve.

One cell phone carrier charges $29.75 a month plus $0.15 a minute for local calls. Another carrier charges $19.95 a month and $0.29 a minute for local calls. For how many minutes is the cost of the plans the same?

Let m represent the number of minutes.

Define a variable and write an equation to find each number. Then solve.

One cell phone carrier charges $29.75 a month plus $0.15 a minute for local calls. Another carrier charges $19.95 a month and $0.29 a minute for local calls. For how many minutes is the cost of the plans the same?

Let m represent the number of minutes.

Words: $29.75 + $0.15 for each minute $19.95 + $0.29 for each minuteVariables: 29.75 + .15m 19.95 + .29mEquation: 29.75 + .15m = 19.95 + .29m

Solve: 29.75 + .15m = 19.95 +.29m - .15m -.15m 29.75 = 19.95 + .14m -19.95 = -19.95 9.8 = .14m 70 = m

So, the cost of the plansIs the same for the first 70 minutes

Your turn!Your turn!A. 4x + 9 = 7x

B. -s + 4 = 7s – 3

C. 12.4y + 14 = 6y – 2

D. Twice a number is 220 less than six times the number. What is the number?

A. 4x + 9 = 7x

B. -s + 4 = 7s – 3

C. 12.4y + 14 = 6y – 2

D. Twice a number is 220 less than six times the number. What is the number?

4x + 9 = 7x Check:-4x = -4x 4(3) + 9 = 7(3) 9 = 3x 12 + 9 = 21 3 = x 21 = 21

-s + 4 = 7s – 3 Check:+s +s -.875 + 4 = 7(.875) - 3 4 = 8s – 3 3.125 = 6.125 - 3 +3 + 3 3.125 = 3.125 7 = 8s .875 = s

Y = -2.5 Check: 12.4(-2.5) + 14 = 6(-2.5) – 2 -31 + 14 = -15 – 2 -17 = -17

2n = 6n – 220 Check: 2(55) = 6(55) – 220 n = 55 110 = 330 – 220 110 = 110

Extra Practice by the door on your way out!!

Extra Practice by the door on your way out!!