Solve for x (|4x-2|)/6=7

$\frac{| 4 x - 2 |}{6} = 7$

Step 1

Multiply both sides by $6$ .

$\frac{| 4 x - 2 |}{6} \cdot 6 = 7 \cdot 6$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{| 4 x - 2 |}{6} \cdot 6$ .

Simplify the numerator.

Factor $2$ out of $4 x - 2$ .

Factor $2$ out of $4 x$ .

$\frac{| 2 (2 x) - 2 |}{6} \cdot 6 = 7 \cdot 6$

Factor $2$ out of $- 2$ .

$\frac{| 2 (2 x) + 2 (- 1) |}{6} \cdot 6 = 7 \cdot 6$

Factor $2$ out of $2 (2 x) + 2 (- 1)$ .

$\frac{| 2 (2 x - 1) |}{6} \cdot 6 = 7 \cdot 6$

Apply the distributive property.

$\frac{| 2 (2 x) + 2 \cdot - 1 |}{6} \cdot 6 = 7 \cdot 6$

Multiply $2$ by $2$ .

$\frac{| 4 x + 2 \cdot - 1 |}{6} \cdot 6 = 7 \cdot 6$

Multiply $2$ by $- 1$ .

$\frac{| 4 x - 2 |}{6} \cdot 6 = 7 \cdot 6$

Factor $2$ out of $4 x - 2$ .

Factor $2$ out of $4 x$ .

$\frac{| 2 (2 x) - 2 |}{6} \cdot 6 = 7 \cdot 6$

Factor $2$ out of $- 2$ .

$\frac{| 2 (2 x) + 2 (- 1) |}{6} \cdot 6 = 7 \cdot 6$

Factor $2$ out of $2 (2 x) + 2 (- 1)$ .

$\frac{| 2 (2 x - 1) |}{6} \cdot 6 = 7 \cdot 6$

Remove non-negative terms from the absolute value.

$\frac{2 | 2 x - 1 |}{6} \cdot 6 = 7 \cdot 6$

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{2 | 2 x - 1 |}{6} \cdot 6 = 7 \cdot 6$

Rewrite the expression.

$2 | 2 x - 1 | = 7 \cdot 6$

Simplify the right side.

Multiply $7$ by $6$ .

$2 | 2 x - 1 | = 42$

Step 3

Solve for $x$ .

Divide each term in $2 | 2 x - 1 | = 42$ by $2$ and simplify.

Divide each term in $2 | 2 x - 1 | = 42$ by $2$ .

$\frac{2 | 2 x - 1 |}{2} = \frac{42}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 | 2 x - 1 |}{2} = \frac{42}{2}$

Divide $| 2 x - 1 |$ by $1$ .

$| 2 x - 1 | = \frac{42}{2}$

Simplify the right side.

Divide $42$ by $2$ .

$| 2 x - 1 | = 21$

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

$2 x - 1 = \pm 21$

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.

$2 x - 1 = 21$

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

Add $1$ to both sides of the equation.

$2 x = 21 + 1$

Add $21$ and $1$ .

$2 x = 22$

Divide each term in $2 x = 22$ by $2$ and simplify.

Divide each term in $2 x = 22$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $22$ by $2$ .

$x = 11$

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

$2 x - 1 = - 21$

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

Add $1$ to both sides of the equation.

$2 x = - 21 + 1$

Add $- 21$ and $1$ .

$2 x = - 20$

Divide each term in $2 x = - 20$ by $2$ and simplify.

Divide each term in $2 x = - 20$ by $2$ .

$\frac{2 x}{2} = \frac{- 20}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 20}{2}$

Divide $x$ by $1$ .

$x = \frac{- 20}{2}$

Simplify the right side.

Divide $- 20$ by $2$ .

$x = - 10$

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

$x = 11, - 10$

Solve for x (|4x-2|)/6=7

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