Solve for x 3/4x+3-2x=-1/4+1/2x+5

$\frac{3}{4} x + 3 - 2 x = - \frac{1}{4} + \frac{1}{2} x + 5$

Simplify $\frac{3}{4} x + 3 - 2 x$ .

Combine $\frac{3}{4}$ and $x$ .

$\frac{3 x}{4} + 3 - 2 x = - \frac{1}{4} + \frac{1}{2} x + 5$

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 x}{4} - 2 x \cdot \frac{4}{4} + 3 = - \frac{1}{4} + \frac{1}{2} x + 5$

Simplify terms.

Combine $- 2 x$ and $\frac{4}{4}$ .

$\frac{3 x}{4} + \frac{- 2 x \cdot 4}{4} + 3 = - \frac{1}{4} + \frac{1}{2} x + 5$

Combine the numerators over the common denominator.

$\frac{3 x - 2 x \cdot 4}{4} + 3 = - \frac{1}{4} + \frac{1}{2} x + 5$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $3 x - 2 x \cdot 4$ .

Factor $x$ out of $3 x$ .

$\frac{x \cdot 3 - 2 x \cdot 4}{4} + 3 = - \frac{1}{4} + \frac{1}{2} x + 5$

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

$\frac{x \cdot 3 + x (- 2 \cdot 4)}{4} + 3 = - \frac{1}{4} + \frac{1}{2} x + 5$

Factor $x$ out of $x \cdot 3 + x (- 2 \cdot 4)$ .

$\frac{x (3 - 2 \cdot 4)}{4} + 3 = - \frac{1}{4} + \frac{1}{2} x + 5$

Multiply $- 2$ by $4$ .

$\frac{x (3 - 8)}{4} + 3 = - \frac{1}{4} + \frac{1}{2} x + 5$

Subtract $8$ from $3$ .

$\frac{x \cdot - 5}{4} + 3 = - \frac{1}{4} + \frac{1}{2} x + 5$

Move $- 5$ to the left of $x$ .

$\frac{- 5 \cdot x}{4} + 3 = - \frac{1}{4} + \frac{1}{2} x + 5$

Move the negative in front of the fraction.

$- \frac{5 x}{4} + 3 = - \frac{1}{4} + \frac{1}{2} x + 5$

Simplify $- \frac{1}{4} + \frac{1}{2} x + 5$ .

Combine $\frac{1}{2}$ and $x$ .

$- \frac{5 x}{4} + 3 = - \frac{1}{4} + \frac{x}{2} + 5$

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{5 x}{4} + 3 = \frac{x}{2} - \frac{1}{4} + 5 \cdot \frac{4}{4}$

Combine $5$ and $\frac{4}{4}$ .

$- \frac{5 x}{4} + 3 = \frac{x}{2} - \frac{1}{4} + \frac{5 \cdot 4}{4}$

Combine the numerators over the common denominator.

$- \frac{5 x}{4} + 3 = \frac{x}{2} + \frac{- 1 + 5 \cdot 4}{4}$

Simplify the numerator.

Multiply $5$ by $4$ .

$- \frac{5 x}{4} + 3 = \frac{x}{2} + \frac{- 1 + 20}{4}$

Add $- 1$ and $20$ .

$- \frac{5 x}{4} + 3 = \frac{x}{2} + \frac{19}{4}$

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

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

$- \frac{5 x}{4} + 3 - \frac{x}{2} = \frac{19}{4}$

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

$- \frac{5 x}{4} - \frac{x}{2} \cdot \frac{2}{2} + 3 = \frac{19}{4}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{2}$ by $\frac{2}{2}$ .

$- \frac{5 x}{4} - \frac{x \cdot 2}{2 \cdot 2} + 3 = \frac{19}{4}$

Multiply $2$ by $2$ .

$- \frac{5 x}{4} - \frac{x \cdot 2}{4} + 3 = \frac{19}{4}$

Combine the numerators over the common denominator.

$\frac{- 5 x - x \cdot 2}{4} + 3 = \frac{19}{4}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 5 x - x \cdot 2$ .

Factor $x$ out of $- 5 x$ .

$\frac{x \cdot - 5 - x \cdot 2}{4} + 3 = \frac{19}{4}$

Factor $x$ out of $- x \cdot 2$ .

$\frac{x \cdot - 5 + x (- 1 \cdot 2)}{4} + 3 = \frac{19}{4}$

Factor $x$ out of $x \cdot - 5 + x (- 1 \cdot 2)$ .

$\frac{x (- 5 - 1 \cdot 2)}{4} + 3 = \frac{19}{4}$

Multiply $- 1$ by $2$ .

$\frac{x (- 5 - 2)}{4} + 3 = \frac{19}{4}$

Subtract $2$ from $- 5$ .

$\frac{x \cdot - 7}{4} + 3 = \frac{19}{4}$

Move $- 7$ to the left of $x$ .

$\frac{- 7 \cdot x}{4} + 3 = \frac{19}{4}$

Move the negative in front of the fraction.

$- \frac{7 x}{4} + 3 = \frac{19}{4}$

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

Subtract $3$ from both sides of the equation.

$- \frac{7 x}{4} = \frac{19}{4} - 3$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{7 x}{4} = \frac{19}{4} - 3 \cdot \frac{4}{4}$

Combine $- 3$ and $\frac{4}{4}$ .

$- \frac{7 x}{4} = \frac{19}{4} + \frac{- 3 \cdot 4}{4}$

Combine the numerators over the common denominator.

$- \frac{7 x}{4} = \frac{19 - 3 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 3$ by $4$ .

$- \frac{7 x}{4} = \frac{19 - 12}{4}$

Subtract $12$ from $19$ .

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

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

$- 7 x = 7$

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

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

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

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $7$ by $- 7$ .

$x = - 1$

Solve for x 3/4x+3-2x=-1/4+1/2x+5

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