Questions: This question: 3 point(s) possible Solve the inequality and graph the solution set on a number line. -13 ≤ (2x/3)-15 < -7 The solution set in interval notation is □ Choose the correct graph below. A. B. C. D.

This question: 3 point(s) possible

Solve the inequality and graph the solution set on a number line.
-13 ≤ (2x/3)-15 < -7

The solution set in interval notation is □
Choose the correct graph below.
A. B.
C. D.

Transcript text: This question: 3 point(s) possible Solve the inequality and graph the solution set on a number line. \[ -13 \leq \frac{2 x}{3}-15<-7 \] The solution set in interval notation is $\square$ Choose the correct graph below. A. B. C. D.

Solution

Solution Steps

Step 1: Simplify the Inequality

Given the inequality: \[ -13 \leq \frac{2x}{3} - 15c < -7 \]

First, isolate the term with $ x $ by adding $ 15c $ to all parts of the inequality: \[ -13 + 15c \leq \frac{2x}{3} < -7 + 15c \]

Step 2: Eliminate the Fraction

Multiply all parts of the inequality by 3 to eliminate the fraction: \[ 3(-13 + 15c) \leq 2x < 3(-7 + 15c) \] \[ -39 + 45c \leq 2x < -21 + 45c \]

Step 3: Solve for $ x $

Divide all parts of the inequality by 2 to solve for $ x $: \[ \frac{-39 + 45c}{2} \leq x < \frac{-21 + 45c}{2} \] \[ -19.5 + 22.5c \leq x < -10.5 + 22.5c \]