Solve for x -2/5=x-1/2(3x-8)

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

Rewrite the equation as $x - \frac{1}{2} \cdot (3 x - 8) = - \frac{2}{5}$ .

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

Simplify $x - \frac{1}{2} \cdot (3 x - 8)$ .

Simplify each term.

Apply the distributive property.

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

Multiply $- \frac{1}{2} (3 x)$ .

Multiply $3$ by $- 1$ .

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

Combine $- 3$ and $\frac{1}{2}$ .

$x + \frac{- 3}{2} x - \frac{1}{2} \cdot - 8 = - \frac{2}{5}$

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

$x + \frac{- 3 x}{2} - \frac{1}{2} \cdot - 8 = - \frac{2}{5}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$x + \frac{- 3 x}{2} + \frac{- 1}{2} \cdot - 8 = - \frac{2}{5}$

Factor $2$ out of $- 8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 1$ by $- 4$ .

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

Move the negative in front of the fraction.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Subtract $3 x$ from $x \cdot 2$ .

Reorder $x$ and $2$ .

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

Subtract $3 x$ from $2 \cdot x$ .

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

Move the negative in front of the fraction.

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

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

Subtract $4$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 4$ by $5$ .

$- \frac{x}{2} = \frac{- 2 - 20}{5}$

Subtract $20$ from $- 2$ .

$- \frac{x}{2} = \frac{- 22}{5}$

Move the negative in front of the fraction.

$- \frac{x}{2} = - \frac{22}{5}$

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{x}{2}) = - 2 (- \frac{22}{5})$

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

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

$- 2 \frac{- x}{2} = - 2 (- \frac{22}{5})$

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- x}{2} = - 2 (- \frac{22}{5})$

Cancel the common factor.

$2 \cdot - 1 \frac{- x}{2} = - 2 (- \frac{22}{5})$

Rewrite the expression.

$- - x = - 2 (- \frac{22}{5})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 2 (- \frac{22}{5})$

Multiply $x$ by $1$ .

$x = - 2 (- \frac{22}{5})$

Simplify the right side.

Multiply $- 2 (- \frac{22}{5})$ .

Multiply $- 1$ by $- 2$ .

$x = 2 (\frac{22}{5})$

Combine $2$ and $\frac{22}{5}$ .

$x = \frac{2 \cdot 22}{5}$

Multiply $2$ by $22$ .

$x = \frac{44}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{44}{5}$

Decimal Form:

$x = 8.8$

Mixed Number Form:

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

Solve for x -2/5=x-1/2(3x-8)

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