Quick Check Equations and Inequalities

1. Ms. Hernandez is taking her children and their friends to the movies. She will pay $10 for her adult ticket and $7 for each child ticket. Ms. Hernandez does not want to spend more than $40. Which inequality can be used to find c, the number of child tickets Ms. Hernandez can purchase?

• A. 7 + 10x > 40
• B. 10x – 7 ≤ 40
• C. 10 + 7x > 40
• D. 10 + 7x ≤ 40

2. If x = -3, then which inequality is true?

• F. -5x + 2 ≤ 12
• G. 3x – 7 ≥ −16
• H. 14 + 2x < 5
• J. 1/2 x + 6 > 11

3. The model below represents an equation. Which value of x makes the equation true?

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4. An equation is modeled below using algebra tiles. Which value of x makes the equation true?

• F. x = 1.5
• G. x = -2
• H. x = 2
• J. x = 4

5. Kasey and her sister both sold cookie dough as a school fundraiser. Kasey sold k tubs of cookie dough. Her sister sold three times as many tubs of cookie dough. If they sold a total of 88 tubs of cookie dough, then how many tubs of cookie dough did Kasey sell, k?

• A. 22
• B. 18
• C. 66
• D. 29

6. A courier service charges a $5 pickup fee, plus $0.15 per mile. The total charge to deliver a package was $7.85. How many miles did the courier service travel to deliver the package?

• F. 52 miles
• G. 19 miles
• H. 85 miles
• J. 33 miles

7. Which situation best represents the equation below?

• A. A pool has 26 gallons of water in it. It is filled at a rate of 9 gallons per minute, until there are 179 gallons.
• B. A dairy farm has 179 cows. All the cows are placed in groups of nine. There are 26 groups of cows.
• C. There were 26 boxes for delivery at the post office one morning. By the end of the day, 179 boxes had been added to the delivery pile. The boxes will be delivered in groups of k
• D. A school assembly has 179 students. Nine teachers escort k number of students out of the assembly, until there are 26 students remaining.

8. The number line below represents the solution to which inequality?

• F. -2x + 7 ≥ 8
• G. 7x + 11 ≤ 4
• H. 6x – 9 ≤ −21
• J. -3x – 15 ≤ −27

9. Jeff is three years younger than twice Michael’s age, m. Which equation can be used to find Jeff’s age?

• A. J = 2m – 3
• B. J = 3m – 2
• C. J = 3 – 2m
• D. J = 2 – 3m

10. What is the value of x in this equation? Report your answer to the tenths place.