Modeling and Solving Equations and Inequalities

The model represents an equation.

What value of x makes the equation true?

• 3

• 8

• 6

• 4

A model for an inequality is shown.

What is the solution to this inequality?

• x > −18

• x > 9

• x > 21

• x > −42

Which equation is true when the value of x is −12?

• ½x +22 = 20

• 15 − ½x = 21

• 11 − 2x = 17

• 3x − 19 = −17

Jeff bought a bottle of water for $2. He also bought some hot dogs for $3 each. Jeff did not spend more than $14 on the hot dogs and the bottle of water. Which inequality can be used to find h, the number of hot dogs that Jeff could have bought?

• 3h − 2 ≤ 14

• 3h + 2 ≤ 14

• 3h − 2 ≥ 14

• 3h + 2 ≥ 14

An equation is modeled.

What value of x makes the equation true?

• −1

• 7

• −5

• 1

Which number line represent the solution to the inequality −7x −13 ≥ 8?

• Line A

• Line B

• Line C

• Line D

1. Which situation is best represented by the following equation?

45w + 123.95 = 753.95

• Erica paid $753.95 for dance classes. She paid a $45 registration fee and $123.95 for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes?

• Erica and her sister paid $753.95 for dance classes. Erica paid $123.95 for each week she was enrolled in the classes, and her sister paid $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica and her sister were enrolled in dance classes?

• Erica paid $753.95 for dance classes. She paid a $123.95 registration fee and $45 for each week she was enrolled in the classes. What is w, the number of weeks Erica was enrolled in dance classes?

• Erica paid $753.95 for dance classes. She paid a $123.95 for each week she was enrolled in the classes after using a coupon that gave her $45 off the price per week. What is w, the number of weeks Erica was enrolled in dance classes?

The model represents an equation.

What is the solution for this equation?

• x = 1

• x = –2

• x = –3

• x = 5

The solution to the inequality 5x − 4 > 21 is represented by which number line?

• 
• 
• 
• 

What is the value of x in this equation?

2x + 2 = −52

• −25

• −27