Solve for x 4/10x-2x+8/5=4/5

$\frac{4}{10} x - 2 x + \frac{8}{5} = \frac{4}{5}$

Step 1

Simplify $\frac{4}{10} x - 2 x + \frac{8}{5}$ .

Simplify each term.

Cancel the common factor of $4$ and $10$ .

Factor $2$ out of $4$ .

$\frac{2 (2)}{10} x - 2 x + \frac{8}{5} = \frac{4}{5}$

Cancel the common factors.

Factor $2$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

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

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

Combine the numerators over the common denominator.

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

Combine the numerators over the common denominator.

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

Multiply $5$ by $- 2$ .

$\frac{2 x - 10 x + 8}{5} = \frac{4}{5}$

Subtract $10 x$ from $2 x$ .

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

Factor $8$ out of $- 8 x + 8$ .

Factor $8$ out of $- 8 x$ .

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

Factor $8$ out of $8$ .

$\frac{8 (- x) + 8 (1)}{5} = \frac{4}{5}$

Factor $8$ out of $8 (- x) + 8 (1)$ .

$\frac{8 (- x + 1)}{5} = \frac{4}{5}$

Factor $- 1$ out of $- x$ .

$\frac{8 (- (x) + 1)}{5} = \frac{4}{5}$

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{8 (- (x) - 1 (- 1))}{5} = \frac{4}{5}$

Factor $- 1$ out of $- (x) - 1 (- 1)$ .

$\frac{8 (- (x - 1))}{5} = \frac{4}{5}$

Simplify the expression.

Rewrite $- (x - 1)$ as $- 1 (x - 1)$ .

$\frac{8 (- 1 (x - 1))}{5} = \frac{4}{5}$

Move the negative in front of the fraction.

$- \frac{8 (x - 1)}{5} = \frac{4}{5}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 8 (x - 1) = 4$

Step 3

Divide each term in $- 8 (x - 1) = 4$ by $- 8$ and simplify.

Divide each term in $- 8 (x - 1) = 4$ by $- 8$ .

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

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

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

Divide $x - 1$ by $1$ .

$x - 1 = \frac{4}{- 8}$

Simplify the right side.

Cancel the common factor of $4$ and $- 8$ .

Factor $4$ out of $4$ .

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

Cancel the common factors.

Factor $4$ out of $- 8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 4

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

Add $1$ to both sides of the equation.

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

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Add $- 1$ and $2$ .

$x = \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$

Solve for x 4/10x-2x+8/5=4/5

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