Question

solve the inequality for w.
9w - 14 < 6w - 2
simplify your answer as much as possible.

Explanation:

Step1: Subtract \(6w\) from both sides

To isolate the terms with \(w\), we subtract \(6w\) from both sides of the inequality \(9w - 14 < 6w - 2\). This gives us \(9w - 6w - 14 < 6w - 6w - 2\), which simplifies to \(3w - 14 < -2\).

Step2: Add 14 to both sides

Next, we add 14 to both sides to isolate the term with \(w\). So, \(3w - 14 + 14 < -2 + 14\), which simplifies to \(3w < 12\).

Step3: Divide both sides by 3

Finally, we divide both sides by 3 to solve for \(w\). \(\frac{3w}{3} < \frac{12}{3}\), which simplifies to \(w < 4\).

Answer:

\(w < 4\)