Solve for x (11x)/10+2=(9x)/8

$\frac{11 x}{10} + 2 = \frac{9 x}{8}$

Step 1

Multiply both sides by $8$ .

$(\frac{11 x}{10} + 2) \cdot 8 = \frac{9 x}{8} \cdot 8$

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{11 x}{10} + 2) \cdot 8$ .

Apply the distributive property.

$\frac{11 x}{10} \cdot 8 + 2 \cdot 8 = \frac{9 x}{8} \cdot 8$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

$\frac{11 x}{2 (5)} \cdot 8 + 2 \cdot 8 = \frac{9 x}{8} \cdot 8$

Factor $2$ out of $8$ .

$\frac{11 x}{2 \cdot 5} \cdot (2 \cdot 4) + 2 \cdot 8 = \frac{9 x}{8} \cdot 8$

Cancel the common factor.

$\frac{11 x}{2 \cdot 5} \cdot (2 \cdot 4) + 2 \cdot 8 = \frac{9 x}{8} \cdot 8$

Rewrite the expression.

$\frac{11 x}{5} \cdot 4 + 2 \cdot 8 = \frac{9 x}{8} \cdot 8$

Combine $\frac{11 x}{5}$ and $4$ .

$\frac{11 x \cdot 4}{5} + 2 \cdot 8 = \frac{9 x}{8} \cdot 8$

Multiply.

Multiply $4$ by $11$ .

$\frac{44 x}{5} + 2 \cdot 8 = \frac{9 x}{8} \cdot 8$

Multiply $2$ by $8$ .

$\frac{44 x}{5} + 16 = \frac{9 x}{8} \cdot 8$

Simplify the right side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{44 x}{5} + 16 = \frac{9 x}{8} \cdot 8$

Rewrite the expression.

$\frac{44 x}{5} + 16 = 9 x$

Step 3

Solve for $x$ .

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

Subtract $9 x$ from both sides of the equation.

$\frac{44 x}{5} + 16 - 9 x = 0$

To write $- 9 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{44 x}{5} - 9 x \cdot \frac{5}{5} + 16 = 0$

Combine $- 9 x$ and $\frac{5}{5}$ .

$\frac{44 x}{5} + \frac{- 9 x \cdot 5}{5} + 16 = 0$

Combine the numerators over the common denominator.

$\frac{44 x - 9 x \cdot 5}{5} + 16 = 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $44 x - 9 x \cdot 5$ .

Factor $x$ out of $44 x$ .

$\frac{x \cdot 44 - 9 x \cdot 5}{5} + 16 = 0$

Factor $x$ out of $- 9 x \cdot 5$ .

$\frac{x \cdot 44 + x (- 9 \cdot 5)}{5} + 16 = 0$

Factor $x$ out of $x \cdot 44 + x (- 9 \cdot 5)$ .

$\frac{x (44 - 9 \cdot 5)}{5} + 16 = 0$

Multiply $- 9$ by $5$ .

$\frac{x (44 - 45)}{5} + 16 = 0$

Subtract $45$ from $44$ .

$\frac{x \cdot - 1}{5} + 16 = 0$

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

$\frac{- 1 \cdot x}{5} + 16 = 0$

Move the negative in front of the fraction.

$- \frac{x}{5} + 16 = 0$

Subtract $16$ from both sides of the equation.

$- \frac{x}{5} = - 16$

Multiply both sides of the equation by $- 5$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 5 (- \frac{x}{5})$ .

Cancel the common factor of $5$ .

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

$- 5 \frac{- x}{5} = - 5 \cdot - 16$

Factor $5$ out of $- 5$ .

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

Cancel the common factor.

$5 \cdot - 1 \frac{- x}{5} = - 5 \cdot - 16$

Rewrite the expression.

$- - x = - 5 \cdot - 16$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 5 \cdot - 16$

Multiply $x$ by $1$ .

$x = - 5 \cdot - 16$

Simplify the right side.

Multiply $- 5$ by $- 16$ .

$x = 80$

Solve for x (11x)/10+2=(9x)/8

Related Questions

Support LCMGCF.com by disabling your adblocker.