Solve for x |4x-3|=6

$| 4 x - 3 | = 6$

Step 1

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

$4 x - 3 = \pm 6$

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.

$4 x - 3 = 6$

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

Add $3$ to both sides of the equation.

$4 x = 6 + 3$

Add $6$ and $3$ .

$4 x = 9$

Divide each term in $4 x = 9$ by $4$ and simplify.

Divide each term in $4 x = 9$ by $4$ .

$\frac{4 x}{4} = \frac{9}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{9}{4}$

Divide $x$ by $1$ .

$x = \frac{9}{4}$

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

$4 x - 3 = - 6$

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

Add $3$ to both sides of the equation.

$4 x = - 6 + 3$

Add $- 6$ and $3$ .

$4 x = - 3$

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

$x = \frac{9}{4}, - \frac{3}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{4}, - \frac{3}{4}$

Decimal Form:

$x = 2.25, - 0.75$

Mixed Number Form:

$x = 2 \frac{1}{4}, - \frac{3}{4}$

Solve for x |4x-3|=6

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