QuestionSolve the equation: $|5x - 8| = 32$ . List all solutions, separated by commas.

Studdy Solution

STEP 1

Assumptions1. The equation is $|5x-8|=32$ . The absolute value of a number is the distance of that number from zero on the number line, which is always positive or zero.
3. The absolute value of a number can be written as two separate equations, one positive and one negative.

STEP 2

First, we can write the absolute value equation as two separate equations. One for the positive value and one for the negative value.
$5x-8=32$ $5x-8=-32$

STEP 3

Now, we solve each equation separately. Starting with the first equation, add8 to both sides to isolate $5x$ .
$5x-8+8=32+8$ $5x=40$

STEP 4

Next, divide both sides of the equation by to solve for $x$ .
$x=40/$

STEP 5

Calculate the value of $x$ .
$x=40/5=8$

STEP 6

Now, we solve the second equation. Add8 to both sides to isolate $5x$ .
$5x-8+8=-32+8$ $5x=-24$

STEP 7

Next, divide both sides of the equation by5 to solve for $x$ .
$x=-24/5$

STEP 8

Calculate the value of $x$ .
$x=-24/5=-4.8$ The solutions to the equation $|5x-8|=32$ are $x=8$ and $x=-4.8$ .

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