First, solve for \( \left|a + 3\right| \):

\( \left|a + 3\right| \) - 3 = 2
\( \left|a + 3\right| \) = 2 + 3
\( \left|a + 3\right| \) = 5

The value inside the absolute value brackets can be either positive or negative so (a + 3) must equal + 5 or -5 for \( \left|a + 3\right| \) to equal 5:

So, a = -8 or a = 2.

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{8 + 4 + 7 + 5}{4} \) = \( \frac{24}{4} \) = 6

1

Christine scored 93% on the test meaning she earned 93% of the possible points on the test. There were 360 possible points on the test so she earned 360 x 0.93 = 336 points. Each question is worth 4 points so she got \( \frac{336}{4} \) = 84 questions right.

To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40]. The first few multiples they share are [4, 8, 12, 16, 20] making 4 the smallest multiple 2 and 4 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 2}{2 x 2} \) + \( \frac{8 x 1}{4 x 1} \)

\( \frac{8}{4} \) + \( \frac{8}{4} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{8 + 8}{4} \) = \( \frac{16}{4} \) = 4