Question Solve the absolute value equation $|8+8c| - 14 = -5$

Studdy Solution

STEP 1

Assumptions1. The equation is $|8+8c|-14=-5$ . The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, it is always positive or zero.

STEP 2

First, we need to isolate the absolute value on one side of the equation. We can do this by adding14 to both sides of the equation.
$|8+8c|-14+14=-5+14$

STEP 3

implify the equation.
$|8+8c|=9$

STEP 4

The absolute value of a number can be either positive or negative. Therefore, we can split the equation into two separate equations one where $(8+8c)$ is positive and one where it is negative.
$8+8c=9$ $8+8c=-9$

STEP 5

Now, we can solve each equation separately. Starting with the first equation, subtract8 from both sides.
$8+8c-8=9-8$

STEP 6

implify the equation.
$8c=1$

STEP 7

Divide both sides by to solve for $c$ .
$c=1/$

STEP 8

Now, we will solve the second equation. Subtract8 from both sides.
$8+8c-8=--8$

STEP 9

implify the equation.
$8c=-17$

STEP 10

Divide both sides by8 to solve for $c$ .
$c=-17/8$ The solutions to the equation are $c=/8$ and $c=-17/8$ .

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