Question Find the solution set of the equation $|x-6| + 4 = 10$ .

Studdy Solution

STEP 1

Assumptions
1. The equation given is $|x-6|+4=10$ .
2. We need to find the solution set for the equation, which means all the values of $x$ that satisfy the equation.

STEP 2

First, we need to isolate the absolute value expression on one side of the equation.
$|x-6|+4=10$

STEP 3

Subtract 4 from both sides of the equation to isolate the absolute value expression.
$|x-6|+4-4=10-4$

STEP 4

Simplify both sides of the equation.
$|x-6|=6$

STEP 5

The absolute value equation $|x-6|=6$ can be split into two separate equations because the expression inside the absolute value can be either positive or negative and still satisfy the absolute value.
$x-6=6 \quad \text{or} \quad x-6=-6$

STEP 6

First, let's solve the equation where the expression inside the absolute value is positive.
$x-6=6$

STEP 7

Add 6 to both sides of the equation to solve for $x$ .
$x-6+6=6+6$

STEP 8

Simplify both sides of the equation.
$x=12$

STEP 9

Now, let's solve the equation where the expression inside the absolute value is negative.
$x-6=-6$

STEP 10

Add 6 to both sides of this equation as well.
$x-6+6=-6+6$

STEP 11

Simplify both sides of the equation.
$x=0$

STEP 12

Combine the solutions from STEP_8 and STEP_11 to form the solution set.
The solution set of the equation $|x-6|+4=10$ is $\{0, 12\}$ .

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