Question

1. solve the inequality. 200 ≤ 15.75x + 50 ≤ 400
2. graph the solution on the number line. approximate values as necessary.
3. complete the statement: kali can work between _ and _ hours each week.

Explanation:

Step1: Solve the left - hand side of the compound inequality

Subtract 50 from all parts of the inequality \(200\leq15.75x + 50\leq400\). We get \(200 - 50\leq15.75x+50 - 50\leq400 - 50\), which simplifies to \(150\leq15.75x\leq350\).

Step2: Solve for \(x\)

Divide all parts of the inequality \(150\leq15.75x\leq350\) by 15.75. So, \(\frac{150}{15.75}\leq\frac{15.75x}{15.75}\leq\frac{350}{15.75}\).
\(\frac{150}{15.75}=\frac{150\times\frac{4}{3}}{15.75\times\frac{4}{3}}=\frac{200}{21}\approx9.52\) and \(\frac{350}{15.75}=\frac{350\times\frac{4}{3}}{15.75\times\frac{4}{3}}=\frac{1400}{63}\approx22.22\).
So, \(9.52\leq x\leq22.22\).

Step3: Graph on the number line

On the number line, mark a closed - circle at approximately 9.52 (since the inequality includes equality for the lower bound) and a closed - circle at approximately 22.22, and shade the region between them.

Step4: Complete the statement

Kali can work between 10 (rounding up 9.52) and 22 (rounding down 22.22) hours each week.

Answer:

Kali can work between 10 and 22 hours each week.