Solve for x 3|x-4|=10

$3 | x - 4 | = 10$

Step 1

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

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

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

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

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

Step 2

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

$x - 4 = \pm \frac{10}{3}$

Step 3

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.

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

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

Add $4$ to both sides of the equation.

$x = \frac{10}{3} + 4$

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = \frac{10}{3} + 4 \cdot \frac{3}{3}$

Combine $4$ and $\frac{3}{3}$ .

$x = \frac{10}{3} + \frac{4 \cdot 3}{3}$

Combine the numerators over the common denominator.

$x = \frac{10 + 4 \cdot 3}{3}$

Simplify the numerator.

Multiply $4$ by $3$ .

$x = \frac{10 + 12}{3}$

Add $10$ and $12$ .

$x = \frac{22}{3}$

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

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

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

Add $4$ to both sides of the equation.

$x = - \frac{10}{3} + 4$

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = - \frac{10}{3} + 4 \cdot \frac{3}{3}$

Combine $4$ and $\frac{3}{3}$ .

$x = - \frac{10}{3} + \frac{4 \cdot 3}{3}$

Combine the numerators over the common denominator.

$x = \frac{- 10 + 4 \cdot 3}{3}$

Simplify the numerator.

Multiply $4$ by $3$ .

$x = \frac{- 10 + 12}{3}$

Add $- 10$ and $12$ .

$x = \frac{2}{3}$

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

$x = \frac{22}{3}, \frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{22}{3}, \frac{2}{3}$

Decimal Form:

$x = 7.\overline{3}, 0.\overline{6}$

Mixed Number Form:

$x = 7 \frac{1}{3}, \frac{2}{3}$

Solve for x 3|x-4|=10

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