solving inequalities

Question

Solve the inequality:

– 3 – 6 (4x + 6) ≤ -111

Answer 1

First, you need to distribute the -6 to the numbers inside the parentheses. Multiply -6 and 4, and multiply -6 and 6. You should end up with -3 - 24x - 36 ≤ -111.

Next, combine the like terms on the left side by doing -3 - 36. You should have -24x - 39 ≤ -111.

Then, bring all like terms to the right side by adding 39 on each side. You should have -24x ≤ -72.

Finally, divide both sides by -24 to get x ≥ 3. Remember that when you divide by a negative, the sign changes to the opposite direction.

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Answer 2

-3 - 6(4x + 6) ≤ -111

-3 - 24x - 36 ≤ -111

-24x ≤ -72

x ≥ 3