Solve for x 3/4x+2/5=x-7/10

$\frac{3}{4} x + \frac{2}{5} = x - \frac{7}{10}$

Combine $\frac{3}{4}$ and $x$ .

$\frac{3 x}{4} + \frac{2}{5} = x - \frac{7}{10}$

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

Subtract $x$ from both sides of the equation.

$\frac{3 x}{4} + \frac{2}{5} - x = - \frac{7}{10}$

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

$\frac{3 x}{4} - x \cdot \frac{4}{4} + \frac{2}{5} = - \frac{7}{10}$

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

$\frac{3 x}{4} + \frac{- x \cdot 4}{4} + \frac{2}{5} = - \frac{7}{10}$

Combine the numerators over the common denominator.

$\frac{3 x - x \cdot 4}{4} + \frac{2}{5} = - \frac{7}{10}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $3 x - x \cdot 4$ .

Factor $x$ out of $3 x$ .

$\frac{x \cdot 3 - x \cdot 4}{4} + \frac{2}{5} = - \frac{7}{10}$

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

$\frac{x \cdot 3 + x (- 1 \cdot 4)}{4} + \frac{2}{5} = - \frac{7}{10}$

Factor $x$ out of $x \cdot 3 + x (- 1 \cdot 4)$ .

$\frac{x (3 - 1 \cdot 4)}{4} + \frac{2}{5} = - \frac{7}{10}$

Multiply $- 1$ by $4$ .

$\frac{x (3 - 4)}{4} + \frac{2}{5} = - \frac{7}{10}$

Subtract $4$ from $3$ .

$\frac{x \cdot - 1}{4} + \frac{2}{5} = - \frac{7}{10}$

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{4} + \frac{2}{5} = - \frac{7}{10}$

Move the negative in front of the fraction.

$- \frac{x}{4} + \frac{2}{5} = - \frac{7}{10}$

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

Subtract $\frac{2}{5}$ from both sides of the equation.

$- \frac{x}{4} = - \frac{7}{10} - \frac{2}{5}$

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

$- \frac{x}{4} = - \frac{7}{10} - \frac{2}{5} \cdot \frac{2}{2}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{5}$ by $\frac{2}{2}$ .

$- \frac{x}{4} = - \frac{7}{10} - \frac{2 \cdot 2}{5 \cdot 2}$

Multiply $5$ by $2$ .

$- \frac{x}{4} = - \frac{7}{10} - \frac{2 \cdot 2}{10}$

Combine the numerators over the common denominator.

$- \frac{x}{4} = \frac{- 7 - 2 \cdot 2}{10}$

Simplify the numerator.

Multiply $- 2$ by $2$ .

$- \frac{x}{4} = \frac{- 7 - 4}{10}$

Subtract $4$ from $- 7$ .

$- \frac{x}{4} = \frac{- 11}{10}$

Move the negative in front of the fraction.

$- \frac{x}{4} = - \frac{11}{10}$

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{x}{4}) = - 4 (- \frac{11}{10})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 4 (- \frac{x}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{x}{4}$ into the numerator.

$- 4 \frac{- x}{4} = - 4 (- \frac{11}{10})$

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- x}{4} = - 4 (- \frac{11}{10})$

Cancel the common factor.

$4 \cdot - 1 \frac{- x}{4} = - 4 (- \frac{11}{10})$

Rewrite the expression.

$- - x = - 4 (- \frac{11}{10})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 4 (- \frac{11}{10})$

Multiply $x$ by $1$ .

$x = - 4 (- \frac{11}{10})$

Simplify the right side.

Simplify $- 4 (- \frac{11}{10})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{11}{10}$ into the numerator.

$x = - 4 (\frac{- 11}{10})$

Factor $2$ out of $- 4$ .

$x = 2 (- 2) \frac{- 11}{10}$

Factor $2$ out of $10$ .

$x = 2 \cdot - 2 \frac{- 11}{2 \cdot 5}$

Cancel the common factor.

$x = 2 \cdot - 2 \frac{- 11}{2 \cdot 5}$

Rewrite the expression.

$x = - 2 (\frac{- 11}{5})$

Combine $- 2$ and $\frac{- 11}{5}$ .

$x = \frac{- 2 \cdot - 11}{5}$

Multiply $- 2$ by $- 11$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 4.4$

Mixed Number Form:

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

Solve for x 3/4x+2/5=x-7/10

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