Solve for x x/2=1/4+(3x)/4

$\frac{x}{2} = \frac{1}{4} + \frac{3 x}{4}$

Step 1

Multiply both sides by $2$ .

$\frac{x}{2} \cdot 2 = (\frac{1}{4} + \frac{3 x}{4}) \cdot 2$

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x}{2} \cdot 2 = (\frac{1}{4} + \frac{3 x}{4}) \cdot 2$

Rewrite the expression.

$x = (\frac{1}{4} + \frac{3 x}{4}) \cdot 2$

Simplify the right side.

Simplify $(\frac{1}{4} + \frac{3 x}{4}) \cdot 2$ .

Apply the distributive property.

$x = \frac{1}{4} \cdot 2 + \frac{3 x}{4} \cdot 2$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x = \frac{1}{2 (2)} \cdot 2 + \frac{3 x}{4} \cdot 2$

Cancel the common factor.

$x = \frac{1}{2 \cdot 2} \cdot 2 + \frac{3 x}{4} \cdot 2$

Rewrite the expression.

$x = \frac{1}{2} + \frac{3 x}{4} \cdot 2$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x = \frac{1}{2} + \frac{3 x}{2 (2)} \cdot 2$

Cancel the common factor.

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

Rewrite the expression.

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

Reorder $\frac{1}{2}$ and $\frac{3 x}{2}$ .

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

Step 3

Solve for $x$ .

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

Subtract $\frac{3 x}{2}$ from both sides of the equation.

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

To write $x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $x$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Move $2$ to the left of $x$ .

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

Subtract $3 x$ from $2 x$ .

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

Move the negative in front of the fraction.

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

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- x = 1$

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $1$ by $- 1$ .

$x = - 1$

Solve for x x/2=1/4+(3x)/4

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