Question

solve the inequality for u.
-16 ≤ -\frac{1}{4}u - 6
simplify your answer as much as possible.

Explanation:

Step1: Add 6 to both sides

To isolate the term with \( u \), we first add 6 to both sides of the inequality \(-16 \leq -\frac{1}{4}u - 6\). This gives us \(-16 + 6 \leq -\frac{1}{4}u - 6 + 6\), which simplifies to \(-10 \leq -\frac{1}{4}u\).

Step2: Multiply both sides by -4 (and reverse inequality)

When we multiply or divide an inequality by a negative number, we must reverse the inequality sign. So we multiply both sides of \(-10 \leq -\frac{1}{4}u\) by -4. This gives \((-10)\times(-4) \geq -\frac{1}{4}u\times(-4)\), which simplifies to \(40 \geq u\) or \(u \leq 40\).

Answer:

\(u \leq 40\)