Solve for x 8/9-4/7=(2x-8)/63

$\frac{8}{9} - \frac{4}{7} = \frac{2 x - 8}{63}$

Rewrite the equation as $\frac{2 x - 8}{63} = \frac{8}{9} - \frac{4}{7}$ .

$\frac{2 x - 8}{63} = \frac{8}{9} - \frac{4}{7}$

Multiply both sides by $63$ .

$\frac{2 x - 8}{63} \cdot 63 = (\frac{8}{9} - \frac{4}{7}) \cdot 63$

Simplify.

Simplify the left side.

Simplify $\frac{2 x - 8}{63} \cdot 63$ .

Factor $2$ out of $2 x - 8$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x) - 8}{63} \cdot 63 = (\frac{8}{9} - \frac{4}{7}) \cdot 63$

Factor $2$ out of $- 8$ .

$\frac{2 x + 2 \cdot - 4}{63} \cdot 63 = (\frac{8}{9} - \frac{4}{7}) \cdot 63$

Factor $2$ out of $2 x + 2 \cdot - 4$ .

$\frac{2 (x - 4)}{63} \cdot 63 = (\frac{8}{9} - \frac{4}{7}) \cdot 63$

Cancel the common factor of $63$ .

Cancel the common factor.

$\frac{2 (x - 4)}{63} \cdot 63 = (\frac{8}{9} - \frac{4}{7}) \cdot 63$

Rewrite the expression.

$2 (x - 4) = (\frac{8}{9} - \frac{4}{7}) \cdot 63$

Apply the distributive property.

$2 x + 2 \cdot - 4 = (\frac{8}{9} - \frac{4}{7}) \cdot 63$

Multiply $2$ by $- 4$ .

$2 x - 8 = (\frac{8}{9} - \frac{4}{7}) \cdot 63$

Simplify the right side.

Simplify $(\frac{8}{9} - \frac{4}{7}) \cdot 63$ .

To write $\frac{8}{9}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$2 x - 8 = (\frac{8}{9} \cdot \frac{7}{7} - \frac{4}{7}) \cdot 63$

To write $- \frac{4}{7}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$2 x - 8 = (\frac{8}{9} \cdot \frac{7}{7} - \frac{4}{7} \cdot \frac{9}{9}) \cdot 63$

Write each expression with a common denominator of $63$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{8}{9}$ by $\frac{7}{7}$ .

$2 x - 8 = (\frac{8 \cdot 7}{9 \cdot 7} - \frac{4}{7} \cdot \frac{9}{9}) \cdot 63$

Multiply $9$ by $7$ .

$2 x - 8 = (\frac{8 \cdot 7}{63} - \frac{4}{7} \cdot \frac{9}{9}) \cdot 63$

Multiply $\frac{4}{7}$ by $\frac{9}{9}$ .

$2 x - 8 = (\frac{8 \cdot 7}{63} - \frac{4 \cdot 9}{7 \cdot 9}) \cdot 63$

Multiply $7$ by $9$ .

$2 x - 8 = (\frac{8 \cdot 7}{63} - \frac{4 \cdot 9}{63}) \cdot 63$

Combine the numerators over the common denominator.

$2 x - 8 = \frac{8 \cdot 7 - 4 \cdot 9}{63} \cdot 63$

Simplify the numerator.

Multiply $8$ by $7$ .

$2 x - 8 = \frac{56 - 4 \cdot 9}{63} \cdot 63$

Multiply $- 4$ by $9$ .

$2 x - 8 = \frac{56 - 36}{63} \cdot 63$

Subtract $36$ from $56$ .

$2 x - 8 = \frac{20}{63} \cdot 63$

Cancel the common factor of $63$ .

Cancel the common factor.

$2 x - 8 = \frac{20}{63} \cdot 63$

Rewrite the expression.

$2 x - 8 = 20$

Solve for $x$ .

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

Add $8$ to both sides of the equation.

$2 x = 20 + 8$

Add $20$ and $8$ .

$2 x = 28$

Divide each term in $2 x = 28$ by $2$ and simplify.

Divide each term in $2 x = 28$ by $2$ .

$\frac{2 x}{2} = \frac{28}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{28}{2}$

Divide $x$ by $1$ .

$x = \frac{28}{2}$

Simplify the right side.

Divide $28$ by $2$ .

$x = 14$

Solve for x 8/9-4/7=(2x-8)/63

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