Question

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

Explanation:

Step1: Add 9u to both sides

To isolate the variable terms, we add \(9u\) to each side of the inequality \(2 - 9u \geq 14 - 6u\). This gives us \(2 \geq 14 + 3u\) (because \(-9u + 9u = 0\) on the left, and \(-6u + 9u = 3u\) on the right).

Step2: Subtract 14 from both sides

Next, we subtract 14 from both sides to get the constant terms on the left. So, \(2 - 14 \geq 3u\), which simplifies to \(-12 \geq 3u\).

Step3: Divide both sides by 3

Now, we divide both sides by 3 to solve for \(u\). Dividing \(-12\) by 3 gives \(-4\), and dividing \(3u\) by 3 gives \(u\). Remember, when dividing an inequality by a positive number, the direction of the inequality sign remains the same. So we have \(-4 \geq u\), which can also be written as \(u \leq -4\).

Answer:

\(u \leq -4\)