Question

this question has two parts. first, answer part a. then, answer part b.
part a
factory the weekly target output for a factory is 300 to 350 units. the factory operates monday through friday.
enter a compound inequality to represent the target output for one day, x.
part b
solve the inequality.

Explanation:

Part A

Step1: Determine the number of working days

The factory operates from Monday to Friday, so there are 5 working days in a week. Let \( x \) be the daily output. Then the weekly output is \( 5x \).

Step2: Set up the compound inequality

The weekly target output is between 300 and 350 units (inclusive, assuming the target is within this range). So we have the compound inequality \( 300 \leq 5x \leq 350 \).

Step1: Solve the left - hand side of the inequality

We start with the inequality \( 300 \leq 5x \leq 350 \). First, solve \( 300 \leq 5x \). Divide both sides of the inequality \( 300 \leq 5x \) by 5. When we divide an inequality by a positive number, the direction of the inequality sign remains the same. So \( \frac{300}{5}\leq\frac{5x}{5} \), which simplifies to \( 60\leq x \).

Step2: Solve the right - hand side of the inequality

Next, solve \( 5x \leq 350 \). Divide both sides of the inequality \( 5x \leq 350 \) by 5. Since 5 is positive, the inequality sign direction remains the same. So \( \frac{5x}{5}\leq\frac{350}{5} \), which simplifies to \( x\leq70 \).

Step3: Combine the two results

Combining the results from Step 1 and Step 2, we get \( 60\leq x\leq70 \).

Answer:

\( 300 \leq 5x \leq 350 \)

Part B