First, solve for \( \left|x - 6\right| \):

\( \left|x - 6\right| \) + 5 = 7
\( \left|x - 6\right| \) = 7 - 5
\( \left|x - 6\right| \) = 2

The value inside the absolute value brackets can be either positive or negative so (x - 6) must equal + 2 or -2 for \( \left|x - 6\right| \) to equal 2:

So, x = 4 or x = 8.

Use PEMDAS (Parentheses, Exponents, Multipy/Divide, Add/Subtract):

2 + (5 + 5) ÷ 2 x 5 - 3²
P: 2 + (10) ÷ 2 x 5 - 3²
E: 2 + 10 ÷ 2 x 5 - 9
MD: 2 + \( \frac{10}{2} \) x 5 - 9
MD: 2 + \( \frac{50}{2} \) - 9
AS: \( \frac{4}{2} \) + \( \frac{50}{2} \) - 9
AS: \( \frac{54}{2} \) - 9
AS: \( \frac{54 - 18}{2} \)
\( \frac{36}{2} \)
18

Christine scored 98% on the test meaning she earned 98% of the possible points on the test. There were 400 possible points on the test so she earned 400 x 0.98 = 392 points. Each question is worth 4 points so she got \( \frac{392}{4} \) = 98 questions right.

1

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 9 workers at the company now and that's enough to staff 3 crews so there are \( \frac{9}{3} \) = 3 workers on a crew. 8 crews are needed for the busy season which, at 3 workers per crew, means that the roofing company will need 8 x 3 = 24 total workers to staff the crews during the busy season. The company already employs 9 workers so they need to add 24 - 9 = 15 new staff for the busy season.