Which number line represents the solution set for the inequality -4(x + 3) ≤ -2 - 2x?

Solution:

-4(x + 3) ≤ -2 - 2x [Given]

Using the distributive property of multiplication on LHS

-4x-12 ≤ -2 - 2x

By transposing the terms with variables on one side and the constant on the other side

- 4x + 2x ≤ –2 + 12

By further calculation

- 2x ≤ 10

Divide both sides by -2

x ≤ -5

Therefore, x ≤ -5 represents the solution set.

Which number line represents the solution set for the inequality -4(x + 3) ≤ -2 - 2x?

Summary:

The number line which represents the solution set for the inequality -4(x + 3) ≤ -2 - 2x is x ≤ -5.