Solve for x 1/2x=-(5/4x+1)+1/2x

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

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

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

Simplify each term.

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

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

Apply the distributive property.

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

Multiply $- 1$ by $1$ .

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

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

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

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

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

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

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

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

Multiply $2$ by $2$ .

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

Combine the numerators over the common denominator.

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

Add $- 5 x$ and $x \cdot 2$ .

Reorder $x$ and $2$ .

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

Add $- 5 x$ and $2 \cdot x$ .

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

Move the negative in front of the fraction.

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

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

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

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

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

$- \frac{3 x}{4} - 1 - \frac{x}{2} = 0$

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

$- \frac{3 x}{4} - \frac{x}{2} \cdot \frac{2}{2} - 1 = 0$

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

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

$- \frac{3 x}{4} - \frac{x \cdot 2}{2 \cdot 2} - 1 = 0$

Multiply $2$ by $2$ .

$- \frac{3 x}{4} - \frac{x \cdot 2}{4} - 1 = 0$

Combine the numerators over the common denominator.

$\frac{- 3 x - x \cdot 2}{4} - 1 = 0$

Simplify each term.

Simplify the numerator.

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

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

$\frac{x \cdot - 3 - x \cdot 2}{4} - 1 = 0$

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

$\frac{x \cdot - 3 + x (- 1 \cdot 2)}{4} - 1 = 0$

Factor $x$ out of $x \cdot - 3 + x (- 1 \cdot 2)$ .

$\frac{x (- 3 - 1 \cdot 2)}{4} - 1 = 0$

Multiply $- 1$ by $2$ .

$\frac{x (- 3 - 2)}{4} - 1 = 0$

Subtract $2$ from $- 3$ .

$\frac{x \cdot - 5}{4} - 1 = 0$

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

$\frac{- 5 \cdot x}{4} - 1 = 0$

Move the negative in front of the fraction.

$- \frac{5 x}{4} - 1 = 0$

Add $1$ to both sides of the equation.

$- \frac{5 x}{4} = 1$

Multiply both sides of the equation by $- \frac{4}{5}$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{4}{5} (- \frac{5 x}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{4}{5}$ into the numerator.

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

Move the leading negative in $- \frac{5 x}{4}$ into the numerator.

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

Factor $4$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $5$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Multiply $- 1$ by $1$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.8$

Solve for x 1/2x=-(5/4x+1)+1/2x

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