Math 7 Ext SOL Mini Quiz 5 Solving Equations and Inequalities

A landscaper charges each customer a flat rate of $150 to develop a plan for the landscaping of an outdoor space. The landscaper also charges $22.50 for each hour of manual labor invested in the landscaping. Write an equation to represent the relationship between the number of hours of manual labor, x, and the total cost, y, for the customer to plan and landscape an outdoor space.

• y = 22.5x + 150

• y = 150x + 22.5

• y = 172.5x

• 150y = 22.5x

What value of x satisfies –3(x + 4) = 2x + 8?

• –4

• 4

Jane and Camila were asked to solve the equation 2x – 4 = 2(–5x + 1). They believe the answer is x = 1/2. Their teacher asked them to both confirm their solution. Their work is shown.

Which statement is the most accurate about their work?

• A. Jane correctly confirmed her solution by double-checking her work and re-solving the problem.

• B. Jane correctly confirmed her solution by replacing the variable with her solution and proving equivalency.

• C. Camila correctly confirmed her solution by double-checking her work and re-solving the problem.

• D. Camila correctly confirmed her solution by replacing the variable with her solution and proving equivalency.

Which verbal situation can be represented by the following equation?

4(x + 6) + 15 = 55

• Mia and her 3 friends went to a movie. Each person paid for 6 tickets plus $1 for snacks. The group also bought a large popcorn for $15. The total was $55. How much did each ticket cost?

• Mia and her 3 friends went to a movie. Each person paid for 1 ticket plus $6 for snacks. The group also bought a pizza for $15. The total was $55. How much did each ticket cost?

• Mia and her 4 friends went to a movie. Each person paid for 1 ticket plus $6 for snacks. The group also bought a large popcorn for $15. The total was $55. How much did each ticket cost?

• Mia and her 4 friends went to a movie. Each person paid for 6 tickets plus $1 for snacks. The group also bought a drink for $15. The total was $55. How much did each ticket cost?

Liam spent $30 on the items included in three gift bags. Each gift bag contains a toy that costs $8.00 and two candy bars. What is the cost of each candy bar?

• $2.00

• $3.50

• $1.00

• $5.00

What is the solution to

22 ≥ 5(x − 2) + 3x?

• A. 4 ≤ x

• B. 16 ≥ x

• C. 16 ≤ x

• D. 4 ≥ x

Which graph best describes the solution set for 6.5x + 9 ≤ 4.5x + 7?

• A

• B

• C

• D

Identify each value of x that makes the following true.

10x – 8 > 2(4x + 2)

WHEH ANSWERING, PLACE A COMMA AND SPACE BETWEEN YOUR ANSWERS

Example: -1, 3 or 20, 11, -22

Fredy has $500 in his bank account and deposits $25 every week. Julia has $300 in her bank account and deposits $40 every week. What is the minimum number of weeks before Julia has more money than Fredy?

Answer: ? weeks or ?

A gym charges $30 per month for membership and a one-time registration fee of $20. Jamie wants to spend less than $200 on gym membership. The inequality 30𝑥 + 20 < 200 represents this situation, where x is the number of months Jamie stays a member. What does the solution x < 6 mean in this situation?

• Jamie must stay a member for exactly 6 months to stay within the budget.

• Jamie must stay a member for at least 6 months to stay within the budget.

• Jamie must stay a member for at most 6 months to stay within the budget.

• Jamie must stay a member for less than 6 months to stay within the budget.