Questions: Solve the compound inequality. -12 ≤ 8x-12 ≤ 12 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is [0,3] (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The solution set is ∅.

Solve the compound inequality.
-12 ≤ 8x-12 ≤ 12

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is [0,3]
(Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.)
B. The solution set is ∅.
Transcript text: Solve the compound inequality. \[ -12 \leq 8 x-12 \leq 12 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution set is [0,3] (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The solution set is $\varnothing$.
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Solution

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Solution Steps

Step 1: Break the compound inequality into two parts

The given compound inequality is: \[ -12 \leq 8x - 12 \leq 12 \] This can be split into two separate inequalities:

  1. \(-12 \leq 8x - 12\)
  2. \(8x - 12 \leq 12\)
Step 2: Solve the first inequality \(-12 \leq 8x - 12\)

Add \(12\) to both sides of the inequality: \[ -12 + 12 \leq 8x - 12 + 12 \] Simplify: \[ 0 \leq 8x \] Divide both sides by \(8\): \[ 0 \leq x \]

Step 3: Solve the second inequality \(8x - 12 \leq 12\)

Add \(12\) to both sides of the inequality: \[ 8x - 12 + 12 \leq 12 + 12 \] Simplify: \[ 8x \leq 24 \] Divide both sides by \(8\): \[ x \leq 3 \]

Step 4: Combine the results

From Step 2 and Step 3, we have: \[ 0 \leq x \leq 3 \] This means the solution set is \([0, 3]\).

Final Answer

\(\boxed{[0, 3]}\)

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