Solve for x 3.5|6x-2|=3.5

$3.5 | 6 x - 2 | = 3.5$

Step 1

Divide each term in $3.5 | 6 x - 2 | = 3.5$ by $3.5$ and simplify.

Divide each term in $3.5 | 6 x - 2 | = 3.5$ by $3.5$ .

$\frac{3.5 | 6 x - 2 |}{3.5} = \frac{3.5}{3.5}$

Simplify the left side.

Cancel the common factor of $3.5$ .

Cancel the common factor.

$\frac{3.5 | 6 x - 2 |}{3.5} = \frac{3.5}{3.5}$

Divide $| 6 x - 2 |$ by $1$ .

$| 6 x - 2 | = \frac{3.5}{3.5}$

Simplify the right side.

Divide $3.5$ by $3.5$ .

$| 6 x - 2 | = 1$

Step 2

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

$6 x - 2 = \pm 1$

Step 3

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.

$6 x - 2 = 1$

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

Add $2$ to both sides of the equation.

$6 x = 1 + 2$

Add $1$ and $2$ .

$6 x = 3$

Divide each term in $6 x = 3$ by $6$ and simplify.

Divide each term in $6 x = 3$ by $6$ .

$\frac{6 x}{6} = \frac{3}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{3}{6}$

Divide $x$ by $1$ .

$x = \frac{3}{6}$

Simplify the right side.

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$x = \frac{3 (1)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$x = \frac{3 \cdot 1}{3 \cdot 2}$

Cancel the common factor.

$x = \frac{3 \cdot 1}{3 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{2}$

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

$6 x - 2 = - 1$

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

Add $2$ to both sides of the equation.

$6 x = - 1 + 2$

Add $- 1$ and $2$ .

$6 x = 1$

Divide each term in $6 x = 1$ by $6$ and simplify.

Divide each term in $6 x = 1$ by $6$ .

$\frac{6 x}{6} = \frac{1}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{1}{6}$

Divide $x$ by $1$ .

$x = \frac{1}{6}$

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

$x = \frac{1}{2}, \frac{1}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}, \frac{1}{6}$

Decimal Form:

$x = 0.5, 0.1\overline{6}$

Solve for x 3.5|6x-2|=3.5

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