Question

bob is working on a report. so far, he has worked on it for 5 hours. he will work on it less than 8 additional hours. lets look at the possible total numbers of hours bob will work on the report.
(a) fill in the blanks to write an inequality that can be used to find x, the total number of hours bob will work on the report. choose only from 5 + x, 5 - x, x - 5, 5x, \\(\frac{5}{x}\\), \\(\frac{x}{5}\\), <, ≤, >, ≥, or 8.
(b) find the possible total numbers of hours bob will work on the report. write your answer as an inequality solved for x.
(c) on the number line below, graph the solution that represents the possible total numbers of hours bob will work on the report.

Explanation:

Step1: Define total hours relation

Let $x$ = total hours. Additional hours = $x - 5$.

Step2: Set up inequality

Additional hours < 8, so $x - 5 < 8$.

Step3: Solve for total hours

Add 5 to both sides: $x - 5 + 5 < 8 + 5$
$x < 13$
Also, total hours > 5 (since he already worked 5 hours), so $5 < x < 13$.

Step4: Graph the solution

Open circle at 5, open circle at 13, shade the region between them on the number line.

Answer:

(a) Inequality: $x - 5 < 8$
(b) $5 < x < 13$
(c) Draw an open circle at 5 and an open circle at 13 on the number line, then shade the interval between these two points.