Solve for x 4-2x=8+x/2

$4 - 2 x = 8 + \frac{x}{2}$

Step 1

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

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

$4 - 2 x - \frac{x}{2} = 8$

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

$4 - 2 x \cdot \frac{2}{2} - \frac{x}{2} = 8$

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

$4 + \frac{- 2 x \cdot 2}{2} - \frac{x}{2} = 8$

Combine the numerators over the common denominator.

$4 + \frac{- 2 x \cdot 2 - x}{2} = 8$

Simplify each term.

Simplify the numerator.

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

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

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

Factor $x$ out of $- x$ .

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

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

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

Multiply $- 2$ by $2$ .

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

Subtract $1$ from $- 4$ .

$4 + \frac{x \cdot - 5}{2} = 8$

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

$4 + \frac{- 5 \cdot x}{2} = 8$

Move the negative in front of the fraction.

$4 - \frac{5 x}{2} = 8$

Step 2

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

Subtract $4$ from both sides of the equation.

$- \frac{5 x}{2} = 8 - 4$

Subtract $4$ from $8$ .

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

Step 3

Multiply both sides of the equation by $- \frac{2}{5}$ .

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

Step 4

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

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

Move the leading negative in $- \frac{5 x}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $5$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Simplify $- \frac{2}{5} \cdot 4$ .

Multiply $- \frac{2}{5} \cdot 4$ .

Multiply $4$ by $- 1$ .

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

Combine $- 4$ and $\frac{2}{5}$ .

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

Multiply $- 4$ by $2$ .

$x = \frac{- 8}{5}$

Move the negative in front of the fraction.

$x = - \frac{8}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{8}{5}$

Decimal Form:

$x = - 1.6$

Mixed Number Form:

$x = - 1 \frac{3}{5}$

Solve for x 4-2x=8+x/2

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