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

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

The value inside the absolute value brackets can be either positive or negative so (c - 7) must equal + 2 or -2 for \( \left|c - 7\right| \) to equal 2:

So, c = 5 or c = 9.

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-5c⁴ - 3c⁴
(-5 - 3)c⁴
-8c⁴

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for time:

time = \( \frac{\text{distance}}{\text{speed}} \)
time = \( \frac{585mi}{65mph} \)
9 hours

To fill a 4 gallon tank exactly halfway you'll need 2 gallons of fuel. Each fuel can holds 1 gallons so:

cans = \( \frac{2 \text{ gallons}}{1 \text{ gallons}} \) = 2