Question

jina is working on a report. so far, she has worked on it for 9 hours. she will work on it less than 4 additional hours. lets look at the possible total numbers of hours jina 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 jina will work on the report. choose only from 9 + x, 9 - x, x - 9, 9x, x/9, 9/x, <, ≤, >, ≥, or 4. inequality: (b) find the possible total numbers of hours jina 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 jina will work on the report.

Explanation:

Step1: Analyze the problem

Jina has already worked 9 hours and will work less than 4 additional hours. Let \(x\) be the total number of hours. The number of additional hours is \(x - 9\), and we know \(x-9<4\).

Step2: Solve the inequality for \(x\)

Add 9 to both sides of the inequality \(x - 9<4\). Using the addition - property of inequalities, we get \(x-9 + 9<4 + 9\), which simplifies to \(x<13\).

Answer:

a. The inequality is \(x-9<4\).
b. The solved - for - \(x\) inequality is \(x<13\).
c. To graph the solution on a number line: Draw a number line. Mark a open circle at 13 (because \(x\) is less than 13, not less than or equal to) and shade the line to the left of 13.