Questions: Solve the inequality. Give the solution in both interval and graph forms. -3 ≤ (2x-6)/4 ≤ 5 The solution to the inequality is (-3,13).

Solve the inequality. Give the solution in both interval and graph forms. -3 ≤ (2x-6)/4 ≤ 5 The solution to the inequality is (-3,13).
Transcript text: Solve the inequality. Give the solution in both interval and graph forms. \[ -3 \leq \frac{2 x-6}{4} \leq 5 \] The solution to the inequality is $(-3,13)$. (Type your answer in interval notation)
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Solution

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Solution Steps

Step 1: Multiply by 4

Multiply all parts of the inequality by 4 to eliminate the fraction:

\(4 * -3 \le 4 * \frac{2x - 6}{4} \le 4 * 5\)

\(-12 \le 2x - 6 \le 20\)

Step 2: Add 6

Add 6 to all parts of the inequality:

\(-12 + 6 \le 2x - 6 + 6 \le 20 + 6\)

\(-6 \le 2x \le 26\)

Step 3: Divide by 2

Divide all parts of the inequality by 2:

\(\frac{-6}{2} \le \frac{2x}{2} \le \frac{26}{2}\)

\(-3 \le x \le 13\)

Final Answer

The solution in interval notation is \(\boxed{(-3, 13)}\), which corresponds to graph D.

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