Solving Equations and Inequalities Flashcards
6 cards from real Rise Placement Test practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 6 Solving Equations and Inequalities flashcards as text
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?
Answer: 120 + 35w ≥ 540
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.
Solve the following equation for x: 3(x + 2) - 4 = 2x + 9
Answer: x = 7
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.
Which of the following is the correct solution set for the absolute value inequality |2x - 1| > 7?
Answer: x 4
An absolute value inequality of the form |A| > B is solved by setting up two separate inequalities: A > B or A 7 and 2x - 1 8, then divide by 2 to get x > 4. For the second, add 1 to both sides to get 2x 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?
Answer: 16 miles
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.
What are the solutions to the quadratic equation x² - 3x - 10 = 0?
Answer: x = 5 and x = -2
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.
Solve the inequality: -2(x - 4) < 10
Answer: x > -1
First, distribute the -2: -2x + 8 -1.