Question

Graph the solution of the inequality –3(x + 1) ≤ 6 on the number line.

A. Number lines from minus five to five five by increament of one from left to right and each tick mark is labeled. Shaded part from close circle at minus three to infinity
B. Number lines from minus five by increament of one from left to right and each tick mark is labeled. Shaded part from open circle at minus three to infinity
C. Number lines from minus five by increament of one from left to right and each tick mark is labeled. Shaded part from minus infinity to close circle at minus three
D. Number lines from minus five by increament of one from left to right and each tick mark is labeled. Shaded part from minus infinity to open circle at minus three

Answer 1

Answer: Choice A

Step-by-step explanation

Let's solve for x.

`-3(\text{x}+1) \le 6\\\\-3\text{x}-3 \le 6\\\\-3\text{x} \le 6+3\\\\-3\text{x} \le 9\\\\\text{x} \ge 9/(-3) \ \ \text{ ....... inequality sign flip}\\\\\text{x} \ge -3\\\\`

The inequality sign flips whenever we divide both sides by a negative number.

The number line graph will have a closed filled in circle at -3 and shading to the right. This will visually mean "The solution set is either x = -3 or x > -3". In other words, we can pick -3 or larger.

The diagram is shown below.

The diagram matches with answer choice A