Math Journal 9-301. 2.

3. 4.

Essential Questions: How do we solve equations with variables on both sides? When does an

equation have no solution or many solutions?

Unit 3 Day 3: Solving Equations With

Variables on Both Sides

Solving Equations With Variables on Both Sides

1) Simplify each side separately.

2) Use inverse operations to collect the variables on one side of the equation and the constants on the other side of the equation.3) Continue to solve the equation.

Example 1: Solve the equations.

a) 7x + 19 = -2x + 55 b) 6x + 22 = 3x + 31+ 2x + 2x

9x+ 19 = 55- 19 -19

= 36

9

x = 4

9x

9

- 3x- 3x3x+ 22 = 31

- 22 -22

3x= 9

33

x = 3

Example 2: Solve the equations.

a) 80 – 9y = 6y b) 10c = 24 + 4c

+ 9y+ 9y

80= 15y

15 15

80

15= y

16

3= y

- 4c- 4c

6c= 24

66

c = 4

Example 3: Solve the equation.

4(1 – x) + 3x = -2(x + 1)

+ 3x4- 4x = -2x

- 1x4 = - 2x - 2+ 2x + 2x

= - 2

- 2

4 + x- 4- 4

x = -6

Example 4: Solve the equation.

9(n – 4) – 7n = 5(3n – 2)

- 7n9n- 36 = 15n

- 362n = 15n - 10- 2n - 2n

= 13n - 10

- 10

-36+ 10+ 10

-2 = n

-26= 13n13 13

Equations With No Solution or Infinitely Many Solutions

Happens when the variable is eliminated and you are left with a true or false

statement.True Statement

Example: 5 = 5

Infinitely Many Solutions

(any number substituted for the variable will work)

False Statement

Example: 5 = 2

No Solution(no number

substituted for the variable will work)

Example 5: Solve the equations.

a) x - 2x + 3 = 3 - x b) 5x + 24 = 5(x - 5)-x + 3 = 3 - x

+ x + x

3= 3

true statement

infinitely many solutions

5x + 24= 5x- 25- 5x - 5x

24= -25

false statementno solution

Example 6: Phone Company A charges an activation fee of 36 cents and then 3 cents per minute. Phone Company B charges 6 cents per minute with no activation fee. How long is a call

that costs the same amount no matter which company is used?

.36 + .03x = .06x- .03x- .03x

.36 = .03x

12 = x

.03 .03

If you talk for more than ___ minutes,

Company __ has the

better price.

Example 7: Justin and Tyson are beginning an exercise program to train for football season. Justin weighs 150 pounds and hopes to gain 2

pounds per week. Tyson weighs 195 pounds and hopes to lose 1 pound per week. If the plan works, in how many weeks will the boys weigh the same

amount?Justin Tyson

150 + 2x

+ 1x+ 1x

150 + 3x = 195- 150- 150

3x = 45

x = 15

In 15 weeks,

Justin and Tyson will weigh the

same amount.

= 195 - 1x

Summary

Essential Questions: How do we solve equations with variables on both sides? When does an equation have no solution or many solutions?

Take 1 minute to write 2 sentences answering the essential question.