Solve for x 4/10x-3x+6/5=4/5

$\frac{4}{10} x - 3 x + \frac{6}{5} = \frac{4}{5}$

Step 1

Simplify $\frac{4}{10} x - 3 x + \frac{6}{5}$ .

Simplify each term.

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

Factor $2$ out of $4$ .

$\frac{2 (2)}{10} x - 3 x + \frac{6}{5} = \frac{4}{5}$

Cancel the common factors.

Factor $2$ out of $10$ .

$\frac{2 \cdot 2}{2 \cdot 5} x - 3 x + \frac{6}{5} = \frac{4}{5}$

Cancel the common factor.

$\frac{2 \cdot 2}{2 \cdot 5} x - 3 x + \frac{6}{5} = \frac{4}{5}$

Rewrite the expression.

$\frac{2}{5} x - 3 x + \frac{6}{5} = \frac{4}{5}$

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

$\frac{2 x}{5} - 3 x + \frac{6}{5} = \frac{4}{5}$

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{2 x}{5} - 3 x \cdot \frac{5}{5} + \frac{6}{5} = \frac{4}{5}$

Combine $- 3 x$ and $\frac{5}{5}$ .

$\frac{2 x}{5} + \frac{- 3 x \cdot 5}{5} + \frac{6}{5} = \frac{4}{5}$

Combine the numerators over the common denominator.

$\frac{2 x - 3 x \cdot 5}{5} + \frac{6}{5} = \frac{4}{5}$

Combine the numerators over the common denominator.

$\frac{2 x - 3 x \cdot 5 + 6}{5} = \frac{4}{5}$

Multiply $5$ by $- 3$ .

$\frac{2 x - 15 x + 6}{5} = \frac{4}{5}$

Subtract $15 x$ from $2 x$ .

$\frac{- 13 x + 6}{5} = \frac{4}{5}$

Factor $- 1$ out of $- 13 x$ .

$\frac{- (13 x) + 6}{5} = \frac{4}{5}$

Rewrite $6$ as $- 1 (- 6)$ .

$\frac{- (13 x) - 1 (- 6)}{5} = \frac{4}{5}$

Factor $- 1$ out of $- (13 x) - 1 (- 6)$ .

$\frac{- (13 x - 6)}{5} = \frac{4}{5}$

Simplify the expression.

Rewrite $- (13 x - 6)$ as $- 1 (13 x - 6)$ .

$\frac{- 1 (13 x - 6)}{5} = \frac{4}{5}$

Move the negative in front of the fraction.

$- \frac{13 x - 6}{5} = \frac{4}{5}$

Step 2

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

$- (13 x - 6) = 4$

Step 3

Simplify $- (13 x - 6)$ .

Apply the distributive property.

$- (13 x) - - 6 = 4$

Multiply.

Multiply $13$ by $- 1$ .

$- 13 x - - 6 = 4$

Multiply $- 1$ by $- 6$ .

$- 13 x + 6 = 4$

Step 4

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

Subtract $6$ from both sides of the equation.

$- 13 x = 4 - 6$

Subtract $6$ from $4$ .

$- 13 x = - 2$

Step 5

Divide each term in $- 13 x = - 2$ by $- 13$ and simplify.

Divide each term in $- 13 x = - 2$ by $- 13$ .

$\frac{- 13 x}{- 13} = \frac{- 2}{- 13}$

Simplify the left side.

Cancel the common factor of $- 13$ .

Cancel the common factor.

$\frac{- 13 x}{- 13} = \frac{- 2}{- 13}$

Divide $x$ by $1$ .

$x = \frac{- 2}{- 13}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{2}{13}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{13}$

Decimal Form:

$x = 0.\overline{153846}$

Solve for x 4/10x-3x+6/5=4/5

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