Questions: Question 12, 2.5.29 Points: 0 of 1 Save Solve the compound inequality. 3 ≤ 2/9 x+9 ≤ 12 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The solution set is ∅.

$Question 12, 2.5.29 Points: 0 of 1 Save Solve the compound inequality. 3 ≤ 2/9 x+9 ≤ 12 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The solution set is ∅.$

Transcript text: Question 12, 2.5.29 Points: 0 of 1 Save Solve the compound inequality. \[ 3 \leq \frac{2}{9} x+9 \leq 12 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\square$ . (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The solution set is $\varnothing$.

Solution

Solution Steps

Step 1: Subtract 9 from all parts of the inequality

To isolate the term containing $ x $, subtract 9 from all parts of the inequality: \[ 3 - 9 \leq \frac{2}{9}x + 9 - 9 \leq 12 - 9 \] This simplifies to: \[ -6 \leq \frac{2}{9}x \leq 3 \]

Step 2: Multiply all parts of the inequality by $ \frac{9}{2} $

To solve for $ x $, multiply all parts of the inequality by $ \frac{9}{2} $: \[ -6 \cdot \frac{9}{2} \leq x \leq 3 \cdot \frac{9}{2} \] This simplifies to: \[ -27 \leq x \leq \frac{27}{2} \] \[ -27 \leq x \leq 13.5 \]

Step 3: Write the solution in interval notation

The solution set in interval notation is: \[ [-27, 13.5] \]