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

5 + (4 + 4) ÷ 5 x 3 - 2²
P: 5 + (8) ÷ 5 x 3 - 2²
E: 5 + 8 ÷ 5 x 3 - 4
MD: 5 + \( \frac{8}{5} \) x 3 - 4
MD: 5 + \( \frac{24}{5} \) - 4
AS: \( \frac{25}{5} \) + \( \frac{24}{5} \) - 4
AS: \( \frac{49}{5} \) - 4
AS: \( \frac{49 - 20}{5} \)
\( \frac{29}{5} \)
5\(\frac{4}{5}\)

First, solve for \( \left|x - 7\right| \):

\( \left|x - 7\right| \) + 6 = -2
\( \left|x - 7\right| \) = -2 - 6
\( \left|x - 7\right| \) = -8

The value inside the absolute value brackets can be either positive or negative so (x - 7) must equal - 8 or --8 for \( \left|x - 7\right| \) to equal -8:

So, x = 15 or x = -1.

Monica scored 77% on the test meaning she earned 77% of the possible points on the test. There were 200 possible points on the test so she earned 200 x 0.77 = 154 points. Each question is worth 2 points so she got \( \frac{154}{2} \) = 77 questions right.

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

0.0002077 in scientific notation is 2.077 x 10^-4

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