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 the 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 to solve for x. When we divide \(-40>5x\) by 5, we get \(\frac{-40}{5}>\frac{5x}{5}\), which simplifies to \(-8 > x\) or \(x < - 8\).

Answer:

\(x < -8\)