Question

solve the inequality for w.
3w + 16 ≤ -3w - 14
simplify your answer as much as possible.

Explanation:

Step1: Add \(3w\) to both sides

To get all the \(w\) terms on one side, we add \(3w\) to both sides of the inequality \(3w + 16\leq - 3w-14\). This gives us \(3w+3w + 16\leq - 3w + 3w-14\), which simplifies to \(6w+16\leq - 14\).

Step2: Subtract 16 from both sides

Next, we want to isolate the term with \(w\). So we subtract 16 from both sides: \(6w+16 - 16\leq - 14-16\). This simplifies to \(6w\leq - 30\).

Step3: Divide both sides by 6

To solve for \(w\), we divide both sides of the inequality \(6w\leq - 30\) by 6. Since 6 is a positive number, the direction of the inequality sign remains the same. So we have \(\frac{6w}{6}\leq\frac{-30}{6}\), which simplifies to \(w\leq - 5\).

Answer:

\(w\leq - 5\)