Solve for x |12-4x|=11

$| 12 - 4 x | = 11$

Step 1

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

$12 - 4 x = \pm 11$

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.

$12 - 4 x = 11$

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

Subtract $12$ from both sides of the equation.

$- 4 x = 11 - 12$

Subtract $12$ from $11$ .

$- 4 x = - 1$

Divide each term in $- 4 x = - 1$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 1$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 1}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 1}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 1}{- 4}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{1}{4}$

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

$12 - 4 x = - 11$

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

Subtract $12$ from both sides of the equation.

$- 4 x = - 11 - 12$

Subtract $12$ from $- 11$ .

$- 4 x = - 23$

Divide each term in $- 4 x = - 23$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 23$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 23}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 23}{- 4}$

Divide $x$ by $1$ .

$x = \frac{- 23}{- 4}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{23}{4}$

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

$x = \frac{1}{4}, \frac{23}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{4}, \frac{23}{4}$

Decimal Form:

$x = 0.25, 5.75$

Mixed Number Form:

$x = \frac{1}{4}, 5 \frac{3}{4}$

Solve for x |12-4x|=11

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