Solve for x |3x-4|=x

$| 3 x - 4 | = x$

Step 1

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

$3 x - 4 = \pm x$

Step 2

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.

$3 x - 4 = x$

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$3 x - 4 - x = 0$

Subtract $x$ from $3 x$ .

$2 x - 4 = 0$

Add $4$ to both sides of the equation.

$2 x = 4$

Divide each term in $2 x = 4$ by $2$ and simplify.

Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

Divide $x$ by $1$ .

$x = \frac{4}{2}$

Simplify the right side.

Divide $4$ by $2$ .

$x = 2$

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

$3 x - 4 = - x$

Move all terms containing $x$ to the left side of the equation.

Add $x$ to both sides of the equation.

$3 x - 4 + x = 0$

Add $3 x$ and $x$ .

$4 x - 4 = 0$

Add $4$ to both sides of the equation.

$4 x = 4$

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.

$x = 2, 1$

Solve for x |3x-4|=x

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