Question

1. values for the area a of the rectangle shown are 12 ≤ a ≤ 36. write and solve a compound inequality for the value of x. rectangle with length 2x and width 3 compound inequality blank solution blank then the options: 12 ≤ 2x ≤ 36; 12 ≤ 2x + 3 ≤ 36; 12 ≤ 6x ≤ 36; 2 ≤ x ≤ 6; 6 ≤ x ≤ 18; 4.5 ≤ x ≤ 17.5

Explanation:

Step1: Find the area formula

The area \( A \) of a rectangle is length times width. Here, length is \( 2x \) and width is \( 3 \), so \( A = 2x\times3 = 6x \).

Step2: Write the compound inequality

Given \( 12\leq A\leq36 \), substitute \( A = 6x \) to get \( 12\leq 6x\leq36 \).

Step3: Solve the compound inequality

Divide all parts by \( 6 \): \( \frac{12}{6}\leq\frac{6x}{6}\leq\frac{36}{6} \), which simplifies to \( 2\leq x\leq6 \).

Answer:

Compound Inequality: \( 12\leq 6x\leq 36 \)
Solution: \( 2\leq x\leq 6 \)