Question

solve the inequality for u.
2u + 6 ≤ 62 - 5u
simplify your answer as much as possible.

Explanation:

Step1: Add \(5u\) to both sides

To get all the \(u\)-terms on one side, we add \(5u\) to both sides of the inequality \(2u + 6\leq62 - 5u\). This gives \(2u+5u + 6\leq62-5u + 5u\), which simplifies to \(7u+6\leq62\).

Step2: Subtract 6 from both sides

Next, we isolate the term with \(u\) by subtracting 6 from both sides. So, \(7u+6 - 6\leq62 - 6\), which simplifies to \(7u\leq56\).

Step3: Divide both sides by 7

To solve for \(u\), we divide both sides of the inequality \(7u\leq56\) by 7. This gives \(\frac{7u}{7}\leq\frac{56}{7}\), which simplifies to \(u\leq8\).

Answer:

\(u\leq8\)