Equations and Inequalities

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• 5

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You are paid $10 per week to do the dishes and take out the trash. You get an additional $3.50 for every other chore you do. Which equation represents your money earned (y) for doing x chores?

• y = 3.5x

• y = 10 + x

• y = 10 + 35x

• y = 10 + 3.5x

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• 13

• 20

• 27

Which equation represents "two times a number plus five is 15"?

• x + 5 = 15

• 2x + 5 = 15

• x + 2(5) = 15

• 2(x + 5) = 15

Solve the linear inequality.

• x > 1

• x > 5

• x > -1

• x < -1

The Rug store installs carpet for $80 plus $9.50 per square yard of carpet. The Magic Carpet charges $120 for installation and $7.50 per square yard of carpet. Write an inequality that could be used to determine the number of square yards of carpet that need to be installed for The Rug Store to charge more than The Magic Carpet.

• 80+9.50x > 120+7.50x

• 80+9.50x < 120+7.50x

• 80x+9.50 > 120x+7.50

• 80x+9.50 < 120x+7.50

From the problem below determine the keyword that determines the expression for Get Clean: The cost to rent a rug cleaner for a day is $25 plus $15 per hour at Rugs Galore. At Get Clean the rug cleaner costs $45 plus $7 per hour. Write an inequality that can be used to show how many hours you need to rent the rug cleaner so that Get Clean’s charges will be less than Rugs Galore’s charges.

• y = 15x + 25

• y = 25x + 15

• y = 45x + 7

• y = 7x + 45

The cost to rent a rug cleaner for a day is $25 plus $15 per hour.

Write an inequality that can be used to show how many hours (x) you can rent the rug cleaner for so that the charges will be less than $130.

Mathematical Equivalence

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From the problem below determine the keyword that determines the expression for Get Clean: The cost to rent a rug cleaner for a day is $25 plus $15 per hour at Rugs Galore. At Get Clean the rug cleaner costs $45 plus $7 per hour. Write an inequality that can be used to show how many hours you need to rent the rug cleaner so that Get Clean’s charges will be less than Rugs Galore’s charges.

• y = 15x + 25

• y = 25x + 15

• y = 45x + 7

• y = 7x + 45

• add 2 to both sides

• subtract 2 from both sides

• subtract 2 from the left side and add 2 to the right side

• add 2 to the left side and subtract 2 from the right side