Solve for x -2/5(-10x+10)-5/4x=-(-x-1)

$- \frac{2}{5} (- 10 x + 10) - \frac{5}{4} x = - (- x - 1)$

Step 1

Simplify $- \frac{2}{5} \cdot (- 10 x + 10) - \frac{5}{4} x$ .

Simplify each term.

Apply the distributive property.

$- \frac{2}{5} (- 10 x) - \frac{2}{5} \cdot 10 - \frac{5}{4} x = - (- x - 1)$

Cancel the common factor of $5$ .

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

$\frac{- 2}{5} (- 10 x) - \frac{2}{5} \cdot 10 - \frac{5}{4} x = - (- x - 1)$

Factor $5$ out of $- 10 x$ .

$\frac{- 2}{5} (5 (- 2 x)) - \frac{2}{5} \cdot 10 - \frac{5}{4} x = - (- x - 1)$

Cancel the common factor.

$\frac{- 2}{5} (5 (- 2 x)) - \frac{2}{5} \cdot 10 - \frac{5}{4} x = - (- x - 1)$

Rewrite the expression.

$- 2 (- 2 x) - \frac{2}{5} \cdot 10 - \frac{5}{4} x = - (- x - 1)$

Multiply $- 2$ by $- 2$ .

$4 x - \frac{2}{5} \cdot 10 - \frac{5}{4} x = - (- x - 1)$

Cancel the common factor of $5$ .

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

$4 x + \frac{- 2}{5} \cdot 10 - \frac{5}{4} x = - (- x - 1)$

Factor $5$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 2$ by $2$ .

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

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

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

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

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

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

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

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

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

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

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

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

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

Multiply $4$ by $4$ .

$\frac{x (16 - 5)}{4} - 4 = - (- x - 1)$

Subtract $5$ from $16$ .

$\frac{x \cdot 11}{4} - 4 = - (- x - 1)$

Move $11$ to the left of $x$ .

$\frac{11 x}{4} - 4 = - (- x - 1)$

Step 2

Simplify $- (- x - 1)$ .

Apply the distributive property.

$\frac{11 x}{4} - 4 = - - x - - 1$

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$\frac{11 x}{4} - 4 = 1 x - - 1$

Multiply $x$ by $1$ .

$\frac{11 x}{4} - 4 = x - - 1$

Multiply $- 1$ by $- 1$ .

$\frac{11 x}{4} - 4 = x + 1$

Step 3

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

Subtract $x$ from both sides of the equation.

$\frac{11 x}{4} - 4 - x = 1$

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

$\frac{11 x}{4} - x \cdot \frac{4}{4} - 4 = 1$

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

$\frac{11 x}{4} + \frac{- x \cdot 4}{4} - 4 = 1$

Combine the numerators over the common denominator.

$\frac{11 x - x \cdot 4}{4} - 4 = 1$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $11 x - x \cdot 4$ .

Factor $x$ out of $11 x$ .

$\frac{x \cdot 11 - x \cdot 4}{4} - 4 = 1$

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

$\frac{x \cdot 11 + x (- 1 \cdot 4)}{4} - 4 = 1$

Factor $x$ out of $x \cdot 11 + x (- 1 \cdot 4)$ .

$\frac{x (11 - 1 \cdot 4)}{4} - 4 = 1$

Multiply $- 1$ by $4$ .

$\frac{x (11 - 4)}{4} - 4 = 1$

Subtract $4$ from $11$ .

$\frac{x \cdot 7}{4} - 4 = 1$

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

$\frac{7 x}{4} - 4 = 1$

Step 4

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

Add $4$ to both sides of the equation.

$\frac{7 x}{4} = 1 + 4$

Add $1$ and $4$ .

$\frac{7 x}{4} = 5$

Step 5

Multiply both sides of the equation by $\frac{4}{7}$ .

$\frac{4}{7} \cdot \frac{7 x}{4} = \frac{4}{7} \cdot 5$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{7} \cdot \frac{7 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{7} \cdot \frac{7 x}{4} = \frac{4}{7} \cdot 5$

Rewrite the expression.

$\frac{1}{7} (7 x) = \frac{4}{7} \cdot 5$

Cancel the common factor of $7$ .

Factor $7$ out of $7 x$ .

$\frac{1}{7} (7 (x)) = \frac{4}{7} \cdot 5$

Cancel the common factor.

$\frac{1}{7} (7 x) = \frac{4}{7} \cdot 5$

Rewrite the expression.

$x = \frac{4}{7} \cdot 5$

Simplify the right side.

Multiply $\frac{4}{7} \cdot 5$ .

Combine $\frac{4}{7}$ and $5$ .

$x = \frac{4 \cdot 5}{7}$

Multiply $4$ by $5$ .

$x = \frac{20}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{20}{7}$

Decimal Form:

$x = 2.\overline{857142}$

Mixed Number Form:

$x = 2 \frac{6}{7}$

Solve for x -2/5(-10x+10)-5/4x=-(-x-1)

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