Question

a clerk must use the elevator to move boxes of paper. the elevators maximum weight limit is 1451 pounds. if each box of paper weighs 67 pounds and the clerk weighs 149 pounds, use an inequality to find the number of whole boxes she can move on the elevator at one time. a. let x represent the number of boxes. translate into an inequality. fill in the blanks below. clarks weight + number of boxes times weight of each box ≤ elevator maximum weight 149 + x • 67 ≤ 1451 what is the first step in solving the resulting equation for x? a. isolate the variable terms on one side of the inequality and the constant terms on the other side of the inequality b. multiply all terms on both sides by the lcd c. divide each side of the inequality by the constant on the left - hand side of the inequality d. combine like terms

Explanation:

Step1: Set up the inequality

The total weight in the elevator is the clerk's weight plus the weight of the boxes. The clerk weighs 149 pounds, each box weighs 67 pounds, and the number of boxes is \(x\). The maximum weight limit of the elevator is 1451 pounds. So the inequality is \(149 + 67x\leqslant1451\).

Step2: Isolate the variable - first step

The first step in solving for \(x\) in the inequality \(149 + 67x\leqslant1451\) is to isolate the variable - term \(67x\) on one side. We do this by subtracting 149 from both sides of the inequality.
\(149+67x - 149\leqslant1451 - 149\)
\(67x\leqslant1302\)
The first - step operation is to isolate the variable terms on one side of the inequality and the constant terms on the other side.

Answer:

A. Isolate the variable terms on one side of the inequality and the constant terms on the other side
a. \(149+67x\leqslant1451\)
b. The inequality \(149 + 67x\leqslant1451\) means that the combined weight of the clerk (149 pounds) and the \(x\) number of boxes (each weighing 67 pounds) must be less than or equal to the maximum weight limit of the elevator (1451 pounds). Solving this inequality will give the maximum number of whole boxes the clerk can move in the elevator at one time.