Question

solve the inequality for x.\
-2x - 16 > 3x + 24\
simplify your answer as much as possible.

Explanation:

Step1: Add 2x to both sides

To get all x terms on one side, we add \(2x\) to both sides of the inequality \(-2x - 16>3x + 24\). This gives \(-2x+2x - 16>3x + 2x+ 24\), which simplifies to \(-16>5x + 24\).

Step2: Subtract 24 from both sides

Next, we subtract 24 from both sides to isolate the term with x. So, \(-16-24>5x+24 - 24\), which simplifies to \(-40>5x\).

Step3: Divide both sides by 5

Now, we divide both sides by 5. Remember, when dividing an inequality by a positive number, the direction of the inequality sign remains the same. So, \(\frac{-40}{5}>\frac{5x}{5}\), which simplifies to \(-8 > x\) or \(x < - 8\).

Answer:

\(x < -8\)