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

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

Step 1

Simplify $- 2 + \frac{3}{4} x + \frac{1}{2} x$ .

Simplify each term.

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

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

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

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

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

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

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

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

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Add $3 x$ and $x \cdot 2$ .

Reorder $x$ and $2$ .

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

Add $3 x$ and $2 \cdot x$ .

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

Step 2

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

Subtract $2 x$ from both sides of the equation.

$- 2 + \frac{5 x}{4} - 2 x = 0$

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

$- 2 + \frac{5 x}{4} - 2 x \cdot \frac{4}{4} = 0$

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

$- 2 + \frac{5 x}{4} + \frac{- 2 x \cdot 4}{4} = 0$

Combine the numerators over the common denominator.

$- 2 + \frac{5 x - 2 x \cdot 4}{4} = 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $5 x - 2 x \cdot 4$ .

Factor $x$ out of $5 x$ .

$- 2 + \frac{x \cdot 5 - 2 x \cdot 4}{4} = 0$

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

$- 2 + \frac{x \cdot 5 + x (- 2 \cdot 4)}{4} = 0$

Factor $x$ out of $x \cdot 5 + x (- 2 \cdot 4)$ .

$- 2 + \frac{x (5 - 2 \cdot 4)}{4} = 0$

Multiply $- 2$ by $4$ .

$- 2 + \frac{x (5 - 8)}{4} = 0$

Subtract $8$ from $5$ .

$- 2 + \frac{x \cdot - 3}{4} = 0$

Move $- 3$ to the left of $x$ .

$- 2 + \frac{- 3 \cdot x}{4} = 0$

Move the negative in front of the fraction.

$- 2 - \frac{3 x}{4} = 0$

Step 3

Add $2$ to both sides of the equation.

$- \frac{3 x}{4} = 2$

Step 4

Multiply both sides of the equation by $- \frac{4}{3}$ .

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

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{4}{3} (- \frac{3 x}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

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

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

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

Factor $4$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Simplify $- \frac{4}{3} \cdot 2$ .

Multiply $- \frac{4}{3} \cdot 2$ .

Multiply $2$ by $- 1$ .

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

Combine $- 2$ and $\frac{4}{3}$ .

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

Multiply $- 2$ by $4$ .

$x = \frac{- 8}{3}$

Move the negative in front of the fraction.

$x = - \frac{8}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{8}{3}$

Decimal Form:

$x = - 2.\overline{6}$

Mixed Number Form:

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

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

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