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. give the answer as an inequality.
b. explain the meaning of the answer to part a.
what is the next necessary step to solve 67x≤1302 for x?
a. multiply both sides by 1302
b. divide both sides by 1302
c. divide both sides by 67
d. multiply both sides by 67
divide both sides by 67 and simplify.
67x≤1302
67x/67≤1302/67
x≤19.4328358209
(round down to the nearest integer)
therefore, the answer is {x|x≤19} (type an inequality)

Explanation:

Step1: Isolate the variable x

To solve the inequality \(67x\leq1302\), we need to get x alone. We do this by dividing both sides of the inequality by 67 since \(67\) is multiplied by \(x\). When we divide both sides of an inequality by a positive number, the direction of the inequality sign remains the same. So we have \(\frac{67x}{67}\leq\frac{1302}{67}\).

Step2: Calculate the value of x

\(x\leq\frac{1302}{67}= 19.432836\).

Step3: Round down to the nearest integer

We are asked to round down to the nearest integer. So \(x\leq19\).

Answer:

\(x\leq19\)