Solve for x (5x)/7-(7x)/5=24/35

$\frac{5 x}{7} - \frac{7 x}{5} = \frac{24}{35}$

Simplify $\frac{5 x}{7} - \frac{7 x}{5}$ .

To write $\frac{5 x}{7}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5 x}{7} \cdot \frac{5}{5} - \frac{7 x}{5} = \frac{24}{35}$

To write $- \frac{7 x}{5}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{5 x}{7} \cdot \frac{5}{5} - \frac{7 x}{5} \cdot \frac{7}{7} = \frac{24}{35}$

Write each expression with a common denominator of $35$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 x}{7}$ by $\frac{5}{5}$ .

$\frac{5 x \cdot 5}{7 \cdot 5} - \frac{7 x}{5} \cdot \frac{7}{7} = \frac{24}{35}$

Multiply $7$ by $5$ .

$\frac{5 x \cdot 5}{35} - \frac{7 x}{5} \cdot \frac{7}{7} = \frac{24}{35}$

Multiply $\frac{7 x}{5}$ by $\frac{7}{7}$ .

$\frac{5 x \cdot 5}{35} - \frac{7 x \cdot 7}{5 \cdot 7} = \frac{24}{35}$

Multiply $5$ by $7$ .

$\frac{5 x \cdot 5}{35} - \frac{7 x \cdot 7}{35} = \frac{24}{35}$

Combine the numerators over the common denominator.

$\frac{5 x \cdot 5 - 7 x \cdot 7}{35} = \frac{24}{35}$

Simplify the numerator.

Factor $x$ out of $5 x \cdot 5 - 7 x \cdot 7$ .

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

$\frac{x (5 \cdot 5) - 7 x \cdot 7}{35} = \frac{24}{35}$

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

$\frac{x (5 \cdot 5) + x (- 7 \cdot 7)}{35} = \frac{24}{35}$

Factor $x$ out of $x (5 \cdot 5) + x (- 7 \cdot 7)$ .

$\frac{x (5 \cdot 5 - 7 \cdot 7)}{35} = \frac{24}{35}$

Multiply $5$ by $5$ .

$\frac{x (25 - 7 \cdot 7)}{35} = \frac{24}{35}$

Multiply $- 7$ by $7$ .

$\frac{x (25 - 49)}{35} = \frac{24}{35}$

Subtract $49$ from $25$ .

$\frac{x \cdot - 24}{35} = \frac{24}{35}$

Simplify the expression.

Move $- 24$ to the left of $x$ .

$\frac{- 24 \cdot x}{35} = \frac{24}{35}$

Move the negative in front of the fraction.

$- \frac{24 x}{35} = \frac{24}{35}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 24 x = 24$

Divide each term in $- 24 x = 24$ by $- 24$ and simplify.

Divide each term in $- 24 x = 24$ by $- 24$ .

$\frac{- 24 x}{- 24} = \frac{24}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 x}{- 24} = \frac{24}{- 24}$

Divide $x$ by $1$ .

$x = \frac{24}{- 24}$

Simplify the right side.

Divide $24$ by $- 24$ .

$x = - 1$

Solve for x (5x)/7-(7x)/5=24/35

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