Solve for x |4x-1|=6

$| 4 x - 1 | = 6$

Step 1

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

$4 x - 1 = \pm 6$

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.

$4 x - 1 = 6$

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

Add $1$ to both sides of the equation.

$4 x = 6 + 1$

Add $6$ and $1$ .

$4 x = 7$

Divide each term in $4 x = 7$ by $4$ and simplify.

Divide each term in $4 x = 7$ by $4$ .

$\frac{4 x}{4} = \frac{7}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{7}{4}$

Divide $x$ by $1$ .

$x = \frac{7}{4}$

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

$4 x - 1 = - 6$

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

Add $1$ to both sides of the equation.

$4 x = - 6 + 1$

Add $- 6$ and $1$ .

$4 x = - 5$

Divide each term in $4 x = - 5$ by $4$ and simplify.

Divide each term in $4 x = - 5$ by $4$ .

$\frac{4 x}{4} = \frac{- 5}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 5}{4}$

Divide $x$ by $1$ .

$x = \frac{- 5}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{4}$

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

$x = \frac{7}{4}, - \frac{5}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{4}, - \frac{5}{4}$

Decimal Form:

$x = 1.75, - 1.25$

Mixed Number Form:

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

Solve for x |4x-1|=6

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