Solve for x 4/5x-1/4x+14=9/10x

$\frac{4}{5} x - \frac{1}{4} x + 14 = \frac{9}{10} x$

Step 1

Simplify $\frac{4}{5} x - \frac{1}{4} x + 14$ .

Simplify each term.

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

$\frac{4 x}{5} - \frac{1}{4} x + 14 = \frac{9}{10} x$

Combine $x$ and $\frac{1}{4}$ .

$\frac{4 x}{5} - \frac{x}{4} + 14 = \frac{9}{10} x$

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

$\frac{4 x}{5} \cdot \frac{4}{4} - \frac{x}{4} + 14 = \frac{9}{10} x$

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

$\frac{4 x}{5} \cdot \frac{4}{4} - \frac{x}{4} \cdot \frac{5}{5} + 14 = \frac{9}{10} x$

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{4 x}{5}$ by $\frac{4}{4}$ .

$\frac{4 x \cdot 4}{5 \cdot 4} - \frac{x}{4} \cdot \frac{5}{5} + 14 = \frac{9}{10} x$

Multiply $5$ by $4$ .

$\frac{4 x \cdot 4}{20} - \frac{x}{4} \cdot \frac{5}{5} + 14 = \frac{9}{10} x$

Multiply $\frac{x}{4}$ by $\frac{5}{5}$ .

$\frac{4 x \cdot 4}{20} - \frac{x \cdot 5}{4 \cdot 5} + 14 = \frac{9}{10} x$

Multiply $4$ by $5$ .

$\frac{4 x \cdot 4}{20} - \frac{x \cdot 5}{20} + 14 = \frac{9}{10} x$

Combine the numerators over the common denominator.

$\frac{4 x \cdot 4 - x \cdot 5}{20} + 14 = \frac{9}{10} x$

Simplify each term.

Simplify the numerator.

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

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

$\frac{x (4 \cdot 4) - x \cdot 5}{20} + 14 = \frac{9}{10} x$

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

$\frac{x (4 \cdot 4) + x (- 1 \cdot 5)}{20} + 14 = \frac{9}{10} x$

Factor $x$ out of $x (4 \cdot 4) + x (- 1 \cdot 5)$ .

$\frac{x (4 \cdot 4 - 1 \cdot 5)}{20} + 14 = \frac{9}{10} x$

Multiply $4$ by $4$ .

$\frac{x (16 - 1 \cdot 5)}{20} + 14 = \frac{9}{10} x$

Multiply $- 1$ by $5$ .

$\frac{x (16 - 5)}{20} + 14 = \frac{9}{10} x$

Subtract $5$ from $16$ .

$\frac{x \cdot 11}{20} + 14 = \frac{9}{10} x$

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

$\frac{11 x}{20} + 14 = \frac{9}{10} x$

Step 2

Combine $\frac{9}{10}$ and $x$ .

$\frac{11 x}{20} + 14 = \frac{9 x}{10}$

Step 3

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

Subtract $\frac{9 x}{10}$ from both sides of the equation.

$\frac{11 x}{20} + 14 - \frac{9 x}{10} = 0$

To write $- \frac{9 x}{10}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{11 x}{20} - \frac{9 x}{10} \cdot \frac{2}{2} + 14 = 0$

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{9 x}{10}$ by $\frac{2}{2}$ .

$\frac{11 x}{20} - \frac{9 x \cdot 2}{10 \cdot 2} + 14 = 0$

Multiply $10$ by $2$ .

$\frac{11 x}{20} - \frac{9 x \cdot 2}{20} + 14 = 0$

Combine the numerators over the common denominator.

$\frac{11 x - 9 x \cdot 2}{20} + 14 = 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $11 x - 9 x \cdot 2$ .

Factor $x$ out of $11 x$ .

$\frac{x \cdot 11 - 9 x \cdot 2}{20} + 14 = 0$

Factor $x$ out of $- 9 x \cdot 2$ .

$\frac{x \cdot 11 + x (- 9 \cdot 2)}{20} + 14 = 0$

Factor $x$ out of $x \cdot 11 + x (- 9 \cdot 2)$ .

$\frac{x (11 - 9 \cdot 2)}{20} + 14 = 0$

Multiply $- 9$ by $2$ .

$\frac{x (11 - 18)}{20} + 14 = 0$

Subtract $18$ from $11$ .

$\frac{x \cdot - 7}{20} + 14 = 0$

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

$\frac{- 7 \cdot x}{20} + 14 = 0$

Move the negative in front of the fraction.

$- \frac{7 x}{20} + 14 = 0$

Step 4

Subtract $14$ from both sides of the equation.

$- \frac{7 x}{20} = - 14$

Step 5

Multiply both sides of the equation by $- \frac{20}{7}$ .

$- \frac{20}{7} (- \frac{7 x}{20}) = - \frac{20}{7} \cdot - 14$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{20}{7} (- \frac{7 x}{20})$ .

Cancel the common factor of $20$ .

Move the leading negative in $- \frac{20}{7}$ into the numerator.

$\frac{- 20}{7} (- \frac{7 x}{20}) = - \frac{20}{7} \cdot - 14$

Move the leading negative in $- \frac{7 x}{20}$ into the numerator.

$\frac{- 20}{7} \cdot \frac{- 7 x}{20} = - \frac{20}{7} \cdot - 14$

Factor $20$ out of $- 20$ .

$\frac{20 (- 1)}{7} \cdot \frac{- 7 x}{20} = - \frac{20}{7} \cdot - 14$

Cancel the common factor.

$\frac{20 \cdot - 1}{7} \cdot \frac{- 7 x}{20} = - \frac{20}{7} \cdot - 14$

Rewrite the expression.

$\frac{- 1}{7} (- 7 x) = - \frac{20}{7} \cdot - 14$

Cancel the common factor of $7$ .

Factor $7$ out of $- 7 x$ .

$\frac{- 1}{7} (7 (- x)) = - \frac{20}{7} \cdot - 14$

Cancel the common factor.

$\frac{- 1}{7} (7 (- x)) = - \frac{20}{7} \cdot - 14$

Rewrite the expression.

$- - x = - \frac{20}{7} \cdot - 14$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{20}{7} \cdot - 14$

Multiply $x$ by $1$ .

$x = - \frac{20}{7} \cdot - 14$

Simplify the right side.

Simplify $- \frac{20}{7} \cdot - 14$ .

Cancel the common factor of $7$ .

Move the leading negative in $- \frac{20}{7}$ into the numerator.

$x = \frac{- 20}{7} \cdot - 14$

Factor $7$ out of $- 14$ .

$x = \frac{- 20}{7} \cdot (7 (- 2))$

Cancel the common factor.

$x = \frac{- 20}{7} \cdot (7 \cdot - 2)$

Rewrite the expression.

$x = - 20 \cdot - 2$

Multiply $- 20$ by $- 2$ .

$x = 40$

Solve for x 4/5x-1/4x+14=9/10x

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