Solve for x 18=3|4x-10|

$18 = 3 | 4 x - 10 |$

Rewrite the equation as $3 | 4 x - 10 | = 18$ .

$3 | 4 x - 10 | = 18$

Divide each term in $3 | 4 x - 10 | = 18$ by $3$ and simplify.

Divide each term in $3 | 4 x - 10 | = 18$ by $3$ .

$\frac{3 | 4 x - 10 |}{3} = \frac{18}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 | 4 x - 10 |}{3} = \frac{18}{3}$

Divide $| 4 x - 10 |$ by $1$ .

$| 4 x - 10 | = \frac{18}{3}$

Simplify the right side.

Divide $18$ by $3$ .

$| 4 x - 10 | = 6$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$4 x - 10 = \pm 6$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$4 x - 10 = 6$

Move all terms not containing $x$ to the right side of the equation.

Add $10$ to both sides of the equation.

$4 x = 6 + 10$

Add $6$ and $10$ .

$4 x = 16$

Divide each term in $4 x = 16$ by $4$ and simplify.

Divide each term in $4 x = 16$ by $4$ .

$\frac{4 x}{4} = \frac{16}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{16}{4}$

Divide $x$ by $1$ .

$x = \frac{16}{4}$

Simplify the right side.

Divide $16$ by $4$ .

$x = 4$

Next, use the negative value of the $\pm$ to find the second solution.

$4 x - 10 = - 6$

Move all terms not containing $x$ to the right side of the equation.

Add $10$ to both sides of the equation.

$4 x = - 6 + 10$

Add $- 6$ and $10$ .

$4 x = 4$

Divide each term in $4 x = 4$ by $4$ and simplify.

Divide each term in $4 x = 4$ by $4$ .

$\frac{4 x}{4} = \frac{4}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{4}{4}$

Divide $x$ by $1$ .

$x = \frac{4}{4}$

Simplify the right side.

Divide $4$ by $4$ .

$x = 1$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 4, 1$

Solve for x 18=3|4x-10|

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