Question

Solve the following inequality algebraically.

∣x+7∣≤8

Answer 1

x ≤ 1 and x ≥ −15

Explanation:

Solving Absolute Value

• We know that x + 7 ≤ 8 or x + 7 ≥ -8

Condition 1:

Step 1: Subtract 7 from both sides.

• 
  `x + 7 - 7\leq 8 - 7`
• 
  `x\leq 1`

Condition 2:

Step 1: Subtract 7 from both sides.

• 
  `x + 7 - 7\geq -8 - 7`
• 
  `x\geq -15`

Therefore, the answer is x ≤ 1 and x ≥ -15.

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