Questions: Solve the inequality. Then graph the solution. 14 ≤ 8x + 6 ≤ 38

Solve the inequality. Then graph the solution. 14 ≤ 8x + 6 ≤ 38
Transcript text: Solve the inequality. Then graph the solution. \[ 14 \leq 8 x+6 \leq 38 \] Question Help: Written Example Submilt Question
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Solution

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Solution Steps

Step 1: Isolate the variable term

The given inequality is \(14 \leq 8x + 6 \leq 38\). To isolate the variable term, subtract 6 from all parts of the inequality: \[ 14 - 6 \leq 8x + 6 - 6 \leq 38 - 6 \] \[ 8 \leq 8x \leq 32 \]

Step 2: Solve for the variable

Next, divide all parts of the inequality by 8 to solve for \(x\): \[ \frac{8}{8} \leq \frac{8x}{8} \leq \frac{32}{8} \] \[ 1 \leq x \leq 4 \]

Step 3: Graph the solution

The solution to the inequality is \(1 \leq x \leq 4\). On a number line, this is represented by a closed interval from 1 to 4, including both endpoints.

Final Answer

The solution to the inequality is \(1 \leq x \leq 4\).

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