Question

1. da’quan is reading a 532-page book for english. his teacher says that each student must have read at least half of the book by the end of the 1st week. if da’quan reads each of the 7 nights, write and solve an inequality to represent the number of pages he should read each night to meet the teacher’s requirements.

Explanation:

Step1: Define the variable

Let \( x \) be the number of pages Da'Quan reads each night.

Step2: Determine total pages read in a week

He reads for 7 nights, so the total pages read in a week is \( 7x \).

Step3: Set up the inequality

The teacher requires at least half of the 532 - page book to be read. Half of 532 is \( \frac{532}{2}=266 \). So the inequality is \( 7x\geq266 \).

Step4: Solve the inequality

Divide both sides of the inequality \( 7x\geq266 \) by 7: \( x\geq\frac{266}{7} \), and \( \frac{266}{7} = 38 \). So \( x\geq38 \).

Answer:

The inequality is \( 7x\geq266 \) (or \( 7x\geq\frac{532}{2} \)) and the solution is \( x\geq38 \), meaning Da'Quan should read at least 38 pages each night.