Question

Consider the equation.
2x − 5 = − 21
Determine the best TWO steps to solve the equation.
Identify the solution.
(3 points)
 Subtract 5 from both sides of the equation.  Add 5 to both sides of the equation.  Add 2 to both sides of the equation.
 Multiply both sides of the equation with 2.  Divide both sides of the equation with 2.  x = -8  x = 13  x = -13  x = 8

Question 2
Step 1.
Step 2.
Step 3.
A)
Consider the inequality.
5a + 18 < − 27
Correctly order the steps used to solve the inequality.
(3 points)
 Subtract 5 from both sides of the inequality.  Subtract 18 from both sides of the inequality.
 Add 18 to both sides of the inequality.  Multiply by 5 on both sides of the inequality.
 Divide by 5 on both sides of the inequality.  Finally, reverse the inequality.  Finally, do not reverse the inequality.

B) Solve for the solution set: 5a + 18 < − 27 (1 point)

Question 3
Step 1.
Step 2.
Step 3.
A)
Consider the inequality.
−2x + 5 > 7
Correctly order the steps to solve the inequality.
(3 points)
 Add 5 to both sides of the inequality.  Subtract 5 from both sides of the inequality.  Add 2 to both sides of the inequality.
 Multiply by -2 on both sides of the inequality.  Divide by -2 on both sides of the inequality.  Finally, reverse the inequality.
 Finally, do not reverse the inequality.

x .
B)
What is the solution to the inequality?
−2x + 5 > 7
(1 point)
 >  <  =  -1  -2  3  1

Question 4
Step 1.
Step 2.
Step 3.
A)
Consider the inequality.
4x − 9 ≥ − 21
Correctly order the steps used to solve the inequality.
(3 points)
 Subtract 4 on both sides of the inequality.  Subtract 9 on both sides of the inequality.
 Add 9 to both sides of the inequality.  Divide by 4 on both sides of the inequality.
 Multiply by 4 on both sides of the inequality.  Finally, reverse the inequality.  Finally, do not reverse the inequality.

B) Which number line represents the solution of 4x − 9 ≥ − 21? (1 point)

Question 5
A)
An SAT tutoring services charges an initial fee of $500 plus $50 for each additional session. David does not want to spend
more than $700 on tutoring.
Which inequality should be used to determine the number of additional sessions (s) David can schedule?
(1 point)
50s + 500 > 700
50s + 500 < 700
50s + 500 ≤ 700
50s + 500 ≥ 700
B) (1 point)
David can schedule additional sessions.

Question 6
A)
Emma has $26 for her weekend expenses. She spent $12.81, including tax, on a new book. Additionally, she needs to set
aside $10.00 for a lunch outing next week. If stickers cost $0.42 per package, tax included, describe the maximum number of
packages (p) Emma can buy.
Which inequality should be used to solve this problem?
(1 point)
0.42p + 22.81 ≥ 26
0.42p + 2.81 ≤ 26
0.42p + 2.81 ≥ 26
0.42p + 22.81 ≤ 26
B) (1 point)
The maximum number of packages Emma can buy is

Answer 1

Question 1
- Best two steps: Add 5 to both sides; Divide both sides by 2.
- Work: 2x − 5 = −21 → 2x = −16 → x = −8
- Solution: x = −8

Question 2
A) Correct order of steps:
1. Subtract 18 from both sides.
2. Divide by 5 on both sides.
3. Finally, do not reverse the inequality.
B) Solve: 5a + 18 < −27 → 5a < −45 → a < −9
- Solution set: a < −9

Question 3
A) Correct order of steps:
1. Subtract 5 from both sides.
2. Divide by −2 on both sides.
3. Finally, reverse the inequality.
B) Solve: −2x + 5 > 7 → −2x > 2 → x < −1
- Solution: x < −1

Question 4
A) Correct order of steps:
1. Add 9 to both sides.
2. Divide by 4 on both sides.
3. Finally, do not reverse the inequality.
B) Solve: 4x − 9 ≥ −21 → 4x ≥ −12 → x ≥ −3
- Number line: closed dot at −3 with arrow to the right (x ≥ −3)

Question 5
A) Inequality: 50s + 500 ≤ 700
B) Solve: 50s ≤ 200 → s ≤ 4
- David can schedule at most 4 additional sessions.

Question 6
A) Inequality: 0.42p + 22.81 ≤ 26
B) Solve: 0.42p ≤ 3.19 → p ≤ 3.19/0.42 ≈ 7.595 → maximum whole packages = 7
- Emma can buy at most 7 packages.