Question

consider the inequality

5/9w greater than or equal to 8

Determine the solution to the inequality

Answer 1

To solve the inequality \( \frac{5}{9}w \geq 8 \), we start by isolating \( w \).

1. Multiply both sides of the inequality by \( 9 \) to eliminate the fraction:
\[
9 \cdot \left(\frac{5}{9}w\right) \geq 9 \cdot 8
\]

This simplifies to:
\[
5w \geq 72
\]

2. Next, divide both sides by \( 5 \):
\[
w \geq \frac{72}{5}
\]

3. Now, simplify \( \frac{72}{5} \):
\[
\frac{72}{5} = 14.4
\]

Thus, the solution to the inequality is:
\[
w \geq 14.4
\]

In interval notation, the solution can be expressed as:
\[
[14.4, \infty)
\]