Math Journal 10-16Rearrange the equation so that y is a function of x

1. 2.

Solve for x.

3. 4.

Math Journal 10-15Solve the formula for the given variable.

1. 2.

Solve for x.

3. 4.

Unit 3 Day 7: Solving Inequalities with Variables on

Both Sides

Essential Questions: How do we solve inequalities with variables on both sides? When does an inequality have no solution

or a solution of all real numbers?

Vocabulary• No solution: when the variable in an equation or inequality is eliminated and you are left with a false statement

• All real numbers: when the variable in an equation or inequality is eliminated and you are left with a true statement

Example 1: Solve the inequalities.

7x + 19 > -2x + 55 6x + 22 < -3x + 31 + 2x+ 2x

9x+ 19> 55

- 19 -19

9x> 36

9 9

x > 4

+ 3x+ 3x

9x+ 22< 31

- 22 -22

9x< 9

9 9

x< 1

Example 2: Solve the inequalities.

x + 2 > 3x + 1 -8x + 7 < 4x – 5

- 3x- 3x

-2x + 2> 1

- 2- 2

-2x> -1

-2 -2

- 4x- 4x

-12x + 7< - 5

- 7- 7

-12x< -12

-12

x <2

1 x > 1

-12

Example 3: Solve the inequality.

(-12x + 16) < 10 – 3(-x – 2)

+ 4-3x < 10

-3x+ 4< 16

- 3x - 3x

-6x + 4< 16

+ 3x

- 4 - 4

-6x< 12

+ 6

+ 3x

-6

x > -2

4

1

-6

Example 4: Solve the inequality.

(12x – 4) < 2(7 – 5x)

- 26x < 14

+ 10x

16x - 2< 14

- 10x

+ 2 + 2

+ 10x

16

x < 1

16x< 16

2

1

16

Example 5: Solve the inequalities.

12 – 2a < - 5a – 9 x – 2x + 3 > 3 – x + 5a+ 5a

12+ 3a< - 9

- 12 - 12

3a< - 21

3 3

a < -7

- x+ 3> 3- x

+ x+ x

3> 3

true statementinfinite solutions

- 5x

< 5x- 25

- 5x

+ 245x

24< -25

false statementno solutions

6y- 3y

3y

+ 6> 5y- 4

- 5y - 5y

> 5y+ 6 - 4

- 6- 6- 4-2y + 6>

-2

Example 6: Solve the inequalities.

5x + 24 < 5(x - 5) 6y - (3y - 6) > 5y - 4

> -10 -2y

y < 5

-2

Example 7: 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. For what value of x is Phone Company A more expensive than Phone

Company B?

.36 + .03x > .06x- .03x- .03x

.36 > .03x

12 > x

Phone Company A is more

expensive when the number of minutes is less than 12. If you talk for more

than 12 minutes, Phone Company A is a

good choice.

.03 .03

x < 12

Example 8: 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,

for how many weeks will Justin weigh less than Tyson?Justin Tyson

150 + 2x

+ 1x+ 1x

150 + 3x < 195- 150- 150

3x < 45

x < 15

Justin will weigh less than Tyson up until the 15

week mark.

< 195 - 1x

3 3

Summary

Essential Questions: How do we solve inequalities with variables on both sides? When does an inequality have no solution or a solution of all real numbers?

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