Question

QUESTION 23 - 1 POINT

Solve: 3|x + 1| ≥-6. Write your solution in interval notation.
(If there is no solution, enter your answer as Ø.)

Answer 1

Sure. Here are the steps on how to solve the equation 3|x + 1| ≥-6:

Divide both sides of the equation by 3.

Simplify both sides of the equation.

Isolate x on the left-hand side of the equation.

Test each solution in the original equation to make sure it makes the equation true.

Write the solution in interval notation.

Here are the detailed steps:

Divide both sides of the equation by 3:

3|x + 1| ≥-6

|x + 1| ≥ -2

Simplify both sides of the equation:

|x + 1| ≥ -2

x + 1 ≥ -2 or x + 1 ≤ -2

Isolate x on the left-hand side of the equation:

x + 1 ≥ -2

x ≥ -2 - 1

x ≥ -3

x + 1 ≤ -2

x ≤ -2 - 1

x ≤ -3

Test each solution in the original equation to make sure it makes the equation true.

Test x = -3 in the original equation:

3|-3 + 1| ≥-6

3|-2| ≥-6

3(2) ≥-6

6 ≥-6

True

Test x = -4 in the original equation: