Question

solve the inequality for u.
24 > -2(3 - u) + 3u
simplify your answer as much as possible.

Explanation:

Step1: Expand the right side

First, we expand \(-2(3 - u)\) using the distributive property \(a(b - c)=ab - ac\). So, \(-2(3 - u)=-6 + 2u\). Then the inequality becomes \(24>-6 + 2u+3u\).

Step2: Combine like terms

Combine the \(u\)-terms on the right side: \(2u + 3u = 5u\). So now the inequality is \(24>-6 + 5u\).

Step3: Add 6 to both sides

To isolate the term with \(u\), we add 6 to both sides of the inequality. \(24 + 6>-6 + 6+5u\), which simplifies to \(30>5u\).

Step4: Divide both sides by 5

Divide both sides of the inequality by 5. \(\frac{30}{5}>\frac{5u}{5}\), which simplifies to \(6>u\) or \(u < 6\).

Answer:

\(u < 6\)