Solve for x x+1/6=4-2x

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

Step 1

Move all terms containing $x$ to the left side of the equation.

Add $2 x$ to both sides of the equation.

$x + \frac{1}{6} + 2 x = 4$

Add $x$ and $2 x$ .

$3 x + \frac{1}{6} = 4$

Step 2

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

Subtract $\frac{1}{6}$ from both sides of the equation.

$3 x = 4 - \frac{1}{6}$

To write $4$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$3 x = 4 \cdot \frac{6}{6} - \frac{1}{6}$

Combine $4$ and $\frac{6}{6}$ .

$3 x = \frac{4 \cdot 6}{6} - \frac{1}{6}$

Combine the numerators over the common denominator.

$3 x = \frac{4 \cdot 6 - 1}{6}$

Simplify the numerator.

Multiply $4$ by $6$ .

$3 x = \frac{24 - 1}{6}$

Subtract $1$ from $24$ .

$3 x = \frac{23}{6}$

Step 3

Divide each term in $3 x = \frac{23}{6}$ by $3$ and simplify.

Divide each term in $3 x = \frac{23}{6}$ by $3$ .

$\frac{3 x}{3} = \frac{\frac{23}{6}}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{\frac{23}{6}}{3}$

Divide $x$ by $1$ .

$x = \frac{\frac{23}{6}}{3}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{23}{6} \cdot \frac{1}{3}$

Multiply $\frac{23}{6} \cdot \frac{1}{3}$ .

Multiply $\frac{23}{6}$ by $\frac{1}{3}$ .

$x = \frac{23}{6 \cdot 3}$

Multiply $6$ by $3$ .

$x = \frac{23}{18}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{23}{18}$

Decimal Form:

$x = 1.2\overline{7}$

Mixed Number Form:

$x = 1 \frac{5}{18}$

Solve for x x+1/6=4-2x

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