Question

-3 - 6(4x + 6) > -111

Explanation:

Step1: Simplify the left side

First, expand \(-6(4x + 6)\) using the distributive property \(a(b + c)=ab+ac\). So \(-6(4x + 6)=-24x-36\). Then the inequality becomes \(-3-24x - 36>-111\). Combine like terms: \(-3 - 36=-39\), so we have \(-24x-39>-111\).

Step2: Isolate the variable term

Add 39 to both sides of the inequality. \(-24x-39 + 39>-111 + 39\), which simplifies to \(-24x>-72\).

Step3: Solve for x

Divide both sides by \(-24\). Remember that when dividing or multiplying an inequality by a negative number, the direction of the inequality sign changes. So \(\frac{-24x}{-24}<\frac{-72}{-24}\), which gives \(x < 3\).

Answer:

\(x < 3\)