Questions: Solve the compound inequality. -6 ≤ 5x - 16 ≤ 4

Solve the compound inequality. -6 ≤ 5x - 16 ≤ 4
Transcript text: Solve the compound inequality. \[ -6 \leq 5 x-16 \leq 4 \]
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Solution

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Solution Steps

To solve the compound inequality \(-6 \leq 5x - 16 \leq 4\), we need to break it into two separate inequalities and solve each one individually. Then, we find the intersection of the solutions to get the final answer.

  1. Solve the first inequality: \(-6 \leq 5x - 16\)
  2. Solve the second inequality: \(5x - 16 \leq 4\)
  3. Combine the solutions from both inequalities to find the range of \(x\).
Step 1: Isolate the variable term in the compound inequality

We start with the given compound inequality: \[ -6 \leq 5x - 16 \leq 4 \]

To isolate the term containing \(x\), we need to add 16 to all parts of the inequality: \[ -6 + 16 \leq 5x - 16 + 16 \leq 4 + 16 \]

Simplifying each part, we get: \[ 10 \leq 5x \leq 20 \]

Step 2: Solve for \(x\)

Next, we divide all parts of the inequality by 5 to solve for \(x\): \[ \frac{10}{5} \leq \frac{5x}{5} \leq \frac{20}{5} \]

Simplifying each part, we get: \[ 2 \leq x \leq 4 \]

Final Answer

The solution to the compound inequality is: \[ \boxed{2 \leq x \leq 4} \]

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