Question

solve the inequality for u.

$6 \leq \frac{u}{7}$

simplify your answer as much as possible.

Explanation:

Step1: Multiply both sides by 7

To solve for \( u \) in the inequality \( 6 \leq \frac{u}{7} \), we multiply both sides of the inequality by 7. This is because we want to isolate \( u \), and multiplying by the denominator (7) will cancel out the division by 7 on the right - hand side. When we multiply both sides of an inequality by a positive number, the direction of the inequality sign remains the same. So we have:
\( 6\times7\leq\frac{u}{7}\times7 \)

Step2: Simplify both sides

Simplifying the left - hand side: \( 6\times7 = 42 \).
Simplifying the right - hand side: \( \frac{u}{7}\times7=u \).
So the inequality becomes \( 42\leq u \), or we can write it as \( u\geq42 \).

Answer:

\( u\geq42 \)