Question

Given the inequality: 2x + 17 ≤ 13

Part 1: Solve the inequality. Write your solution as an inequality comparing the variable to the solution.
Show and/or explain your work.

Answer 1

Start with the inequality:
2x + 17 ≤ 13

Subtract 17 from both sides:
2x ≤ 13 − 17
2x ≤ −4

Divide both sides by 2 (positive, so the inequality sign stays the same):
x ≤ −2

Answer: x ≤ −2

Check: if x = −2, 2(−2)+17 = −4+17 = 13 (satisfies ≤); if x = −3, 2(−3)+17 = −6+17 = 11 ≤ 13 (also satisfies).