Question

1. a) write the word sentence as an inequality.

a number x divided by 7 is less than -3.
the inequality is
b) graph the solution

Explanation:

Step1: Translate the word sentence to inequality

"A number \(x\) divided by \(7\) is less than \(-3\)" can be written as \(\frac{x}{7}<-3\).

Step2: Solve the inequality

Multiply both sides of the inequality \(\frac{x}{7}<-3\) by \(7\). Using the property of inequalities (if \(a < b\) and \(c>0\), then \(ac < bc\)), we get \(x<-21\).

Step3: Graph the solution

On the number - line, since \(x < - 21\), we draw an open circle at \(-21\) (because \(-21\) is not included in the solution set) and shade the part of the number - line to the left of \(-21\).

Answer:

a) The inequality is \(\frac{x}{7}<-3\).
b) To graph the solution: Draw an open circle at \(-21\) on the number - line and shade to the left of \(-21\).