Rise Placement Test Solving Equations and Inequalities Questions and Answers

Question 1

A student is saving for a trip that costs $540. They have already saved $120 and can save an additional $35 per week. Which inequality correctly represents the number of weeks, w, the student still needs to save to have at least enough money for the trip?

Accepted Answer

120 + 35w ≥ 540

Answer

The total amount saved will be the initial $120 plus the amount saved per week ($35) times the number of weeks (w). This total must be 'at least' $540, which translates to 'greater than or equal to' (≥). Therefore, the correct inequality is 120 + 35w ≥ 540.

Question 2

Solve the following equation for x: 3(x + 2) - 4 = 2x + 9

Accepted Answer

x = 7

Answer

First, distribute the 3 on the left side: 3x + 6 - 4 = 2x + 9. Simplify the left side: 3x + 2 = 2x + 9. Next, subtract 2x from both sides: x + 2 = 9. Finally, subtract 2 from both sides to isolate x: x = 7.

Question 3

Which of the following is the correct solution set for the absolute value inequality |2x - 1| > 7?

Accepted Answer

x < -3 or x > 4

Answer

An absolute value inequality of the form |A| > B is solved by setting up two separate inequalities: A > B or A < -B. So, we solve 2x - 1 > 7 and 2x - 1 < -7. For the first, add 1 to both sides to get 2x > 8, then divide by 2 to get x > 4. For the second, add 1 to both sides to get 2x < -6, then divide by 2 to get x < -3. The solution set is x < -3 or x > 4.

Question 4

A taxi company charges a flat fee of $3.00 plus an additional $0.75 per mile. If a passenger has at most $15.00 to spend, what is the maximum number of miles they can travel?

Accepted Answer

16 miles

Answer

Let 'm' be the number of miles. The total cost is represented by the inequality 3.00 + 0.75m ≤ 15.00. To solve, first subtract 3.00 from both sides: 0.75m ≤ 12.00. Then, divide both sides by 0.75: m ≤ 16. The maximum number of miles is 16.

Question 5

What are the solutions to the quadratic equation x² - 3x - 10 = 0?

Accepted Answer

x = 5 and x = -2

Answer

This quadratic equation can be solved by factoring. We need to find two numbers that multiply to -10 and add to -3. These numbers are -5 and +2. So, the equation can be factored as (x - 5)(x + 2) = 0. Using the zero-product property, we set each factor to zero: x - 5 = 0 or x + 2 = 0. Solving these gives x = 5 and x = -2.

Rise Placement Test Practice Test

Rise Placement Test Practice Test

Rise Placement Test Solving Equations and Inequalities Questions and Answers