Solve for x x/7-1=x/9+5

$\frac{x}{7} - 1 = \frac{x}{9} + 5$

Step 1

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

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

$\frac{x}{7} - 1 - \frac{x}{9} = 5$

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

$\frac{x}{7} \cdot \frac{9}{9} - \frac{x}{9} - 1 = 5$

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

$\frac{x}{7} \cdot \frac{9}{9} - \frac{x}{9} \cdot \frac{7}{7} - 1 = 5$

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

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

$\frac{x \cdot 9}{7 \cdot 9} - \frac{x}{9} \cdot \frac{7}{7} - 1 = 5$

Multiply $7$ by $9$ .

$\frac{x \cdot 9}{63} - \frac{x}{9} \cdot \frac{7}{7} - 1 = 5$

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

$\frac{x \cdot 9}{63} - \frac{x \cdot 7}{9 \cdot 7} - 1 = 5$

Multiply $9$ by $7$ .

$\frac{x \cdot 9}{63} - \frac{x \cdot 7}{63} - 1 = 5$

Combine the numerators over the common denominator.

$\frac{x \cdot 9 - x \cdot 7}{63} - 1 = 5$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x \cdot 9 - x \cdot 7$ .

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

$\frac{x (9) - x \cdot 7}{63} - 1 = 5$

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

$\frac{x (9) + x (- 1 \cdot 7)}{63} - 1 = 5$

Factor $x$ out of $x (9) + x (- 1 \cdot 7)$ .

$\frac{x (9 - 1 \cdot 7)}{63} - 1 = 5$

Multiply $- 1$ by $7$ .

$\frac{x (9 - 7)}{63} - 1 = 5$

Subtract $7$ from $9$ .

$\frac{x \cdot 2}{63} - 1 = 5$

Move $2$ to the left of $x$ .

$\frac{2 x}{63} - 1 = 5$

Step 2

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

Add $1$ to both sides of the equation.

$\frac{2 x}{63} = 5 + 1$

Add $5$ and $1$ .

$\frac{2 x}{63} = 6$

Step 3

Multiply both sides of the equation by $\frac{63}{2}$ .

$\frac{63}{2} \cdot \frac{2 x}{63} = \frac{63}{2} \cdot 6$

Step 4

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $63$ .

Cancel the common factor.

$\frac{63}{2} \cdot \frac{2 x}{63} = \frac{63}{2} \cdot 6$

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{63}{2} \cdot 6$

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{63}{2} \cdot 6$

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{63}{2} \cdot 6$

Rewrite the expression.

$x = \frac{63}{2} \cdot 6$

Simplify the right side.

Simplify $\frac{63}{2} \cdot 6$ .

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$x = \frac{63}{2} \cdot (2 (3))$

Cancel the common factor.

$x = \frac{63}{2} \cdot (2 \cdot 3)$

Rewrite the expression.

$x = 63 \cdot 3$

Multiply $63$ by $3$ .

$x = 189$

Solve for x x/7-1=x/9+5

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