Free Rise Placement Test Solving Equations and Inequalities Questions and Answers — Questions and Answers
Question 1: A cell phone plan costs $45 per month, which includes 5 gigabytes of data. Each additional gigabyte of data costs $10. If a customer's bill was $85 for one month, which equation could be used to find the number of additional gigabytes, g, they used?
- 45g + 10 = 85
- 45 + 10g = 85 (Correct answer)
- 55g = 85
- 45 + 5g = 85
Correct answer: 45 + 10g = 85
The base cost of the plan is a fixed $45. The variable cost is $10 for each additional gigabyte, represented by 'g'. Therefore, the total cost is the fixed cost plus the variable cost (10g), which equals the total bill of $85. The correct equation is 45 + 10g = 85.
Question 2: Solve the following inequality: 14 - 3x > 2
- x > 4
- x < -4
- x > -4
- x < 4 (Correct answer)
Correct answer: x < 4
To solve for x, first subtract 14 from both sides to get -3x > -12. Then, divide both sides by -3. When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign. Therefore, x < 4.
Question 3: Which of the following values for 'y' is a solution to the equation 5y - 7 = 3y + 5?
- y = 1
- y = 2
- y = 6 (Correct answer)
- y = -1
Correct answer: y = 6
To solve the equation, first get the variable terms on one side by subtracting 3y from both sides, resulting in 2y - 7 = 5. Next, add 7 to both sides to isolate the variable term: 2y = 12. Finally, divide by 2 to find y = 6.
Question 4: A student needs to have an average score of at least 80 on four tests. Their scores on the first three tests are 75, 82, and 78. What is the minimum score the student must get on the fourth test to achieve an average of at least 80?
- 80
- 85 (Correct answer)
- 75
- 82
Correct answer: 85
Let x be the score on the fourth test. The average is the sum of the scores divided by the number of tests. The inequality is (75 + 82 + 78 + x) / 4 ≥ 80. Simplify the sum: (235 + x) / 4 ≥ 80. Multiply both sides by 4: 235 + x ≥ 320. Subtract 235 from both sides: x ≥ 85. The minimum score required is 85.
Question 5: Which of the following equations is equivalent to 3(x + 5) = 21?
- 3x = 16
- x + 5 = 7 (Correct answer)
- x + 5 = 63
- 3x + 5 = 21
Correct answer: x + 5 = 7
To find an equivalent equation, you can perform the same operation on both sides. Dividing both sides of the original equation by 3 gives x + 5 = 7. This is a valid step in solving the equation and maintains the equality.
Question 6: What is the solution set for the inequality |2x - 3| ≤ 7?
- x ≤ 5
- x ≥ -2 or x ≤ 5
- -5 ≤ x ≤ 2
- -2 ≤ x ≤ 5 (Correct answer)
Correct answer: -2 ≤ x ≤ 5
An absolute value inequality of the form |A| ≤ B is equivalent to -B ≤ A ≤ B. So, we can write -7 ≤ 2x - 3 ≤ 7. To solve this compound inequality, add 3 to all three parts: -4 ≤ 2x ≤ 10. Then, divide all three parts by 2: -2 ≤ x ≤ 5.
Free Rise Placement Test Solving Equations and Inequalities Questions and Answers
A cell phone plan costs $45 per month, which includes 5 gigabytes of data.
Each additional gigabyte of data costs $10.
If a customer's bill was $85 for one month, which equation could be used to find the number of additional gigabytes, g, they used?