Question

.
.
.
.
consider the inequality
5/9w≥ 8
which step is needed to solve this inequality?
a. add 5/9 to both sides of the inequality
b. subtract 5/9 to both sides of the inequality
c. multiply 5/9 on both sides of the inequality
d. divide 5/9 on both sides of the inequality
determined the solution to the inequality
a. w ≥ 7 4/9
b. w ≥ 8 5/9
c. w ≥ 14 2/5
d. w ≥ 4 4/5
how should the solution of the inequality be graphed?
a. open circle, shade right
b. open circle, shade left
c. closed circle, shade right
d. closed circle, shade left

Answer 1

To solve the inequality \( \frac{5}{9}w \geq 8 \), we need to isolate \( w \).

The appropriate step to solve the inequality would be:

**d. divide \( \frac{5}{9} \) on both sides of the inequality.**

Now, let's perform the division:

\[
w \geq \frac{8}{\frac{5}{9}} \\
w \geq 8 \times \frac{9}{5} \\
w \geq \frac{72}{5} \\
w \geq 14.4
\]

Converting \( 14.4 \) to a mixed number gives us \( 14 \frac{2}{5} \).

So the solution to the inequality is:

**c. \( w \geq 14 \frac{2}{5} \)**.

Next, for how to graph the solution of the inequality \( w \geq 14 \frac{2}{5} \):

Since we have a "greater than or equal to" inequality, we should use a closed circle on \( 14 \frac{2}{5} \) and shade to the right to indicate all values greater than or equal to this point.

This means the appropriate choice is:

**c. closed circle, shade right**.