Let's solve the inequality step by step.
Question 1
Given the inequality:
\[ \frac{5}{9}w \geq 8 \]
To isolate \( w \), we need to divide both sides of the inequality by \(\frac{5}{9}\). According to the rules for inequalities, when you divide by a positive number, the direction of the inequality remains the same.
The correct step is:
- Divide \( \frac{5}{9} \) on both sides of the inequality.
Question 2
Now, let's solve for \( w \):
\[ w \geq 8 \div \left(\frac{5}{9}\right) \]
Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[ w \geq 8 \times \frac{9}{5} \]
Calculating that gives:
\[ w \geq \frac{72}{5} = 14.4 \]
Now, \( 14.4 \) can be expressed as a mixed number:
\[ 14.4 = 14 \frac{2}{5} \]
So the solution to the inequality is:
- w ≥ 14 2/5
Question 3
Since the inequality is \( w \geq 14 \frac{2}{5} \), we use a closed circle at \( 14 \frac{2}{5} \), and since \( w \) is greater than or equal to that value, we shade right on the number line.
So, the correct representation is:
- Closed circle, shade right
Summary of Answers
- Divide \( \frac{5}{9} \) on both sides of the inequality.
- w ≥ 14 2/5
- Closed circle, shade right