Graph the set on the number line. Then, write the set using interval notation. 7 |x + 3| ≤ 14

We will solve the inequality to find its solution set and then plot it on a number line.

Answer: The solution set for 7 |x + 3| ≤ 14 using interval notation is [-5, -1]. The graph is shown below.

Let us solve the inequality 7 |x + 3| ≤ 14.

Explanation:

Divide both sides of the inequality 7 |x + 3| ≤ 14 by 7

|x + 3| ≤ 14/7

⇒ |x + 3| ≤ 2

⇒ - 2 ≤ x + 3 ≤ 2

Subtract 3 throughout in - 2 ≤ x + 3 ≤ 2 

⇒ - 2 - 3 ≤ x + 3 - 3 ≤ 2 - 3

⇒ -5 ≤ x ≤ -1

The interval notation to express the set -5 ≤ x ≤ -1 is [-5, -1].

You can use Cuemath's Interval Notation Calculator that helps to plot the set on a number line.

The graph of the solution set is shown below.

Therefore, the solution set for 7 |x + 3| ≤ 14 using interval notation is [-5, -1].