Pre-Algebra Examples

$\frac{5 - x}{x} - \frac{3}{4} = \frac{7}{x}$

Step 1

Simplify $\frac{5 - x}{x} - \frac{3}{4}$ .

Tap for more steps...

Step 1.1

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

$\frac{5 - x}{x} \cdot \frac{4}{4} - \frac{3}{4} = \frac{7}{x}$

Step 1.2

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{5 - x}{x} \cdot \frac{4}{4} - \frac{3}{4} \cdot \frac{x}{x} = \frac{7}{x}$

Step 1.3

Write each expression with a common denominator of $x \cdot 4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.3.1

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

$\frac{(5 - x) \cdot 4}{x \cdot 4} - \frac{3}{4} \cdot \frac{x}{x} = \frac{7}{x}$

Step 1.3.2

Multiply $\frac{3}{4}$ by $\frac{x}{x}$ .

$\frac{(5 - x) \cdot 4}{x \cdot 4} - \frac{3 x}{4 x} = \frac{7}{x}$

Step 1.3.3

Reorder the factors of $x \cdot 4$ .

$\frac{(5 - x) \cdot 4}{4 x} - \frac{3 x}{4 x} = \frac{7}{x}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(5 - x) \cdot 4 - 3 x}{4 x} = \frac{7}{x}$

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Apply the distributive property.

$\frac{5 \cdot 4 - x \cdot 4 - 3 x}{4 x} = \frac{7}{x}$

Step 1.5.2

Multiply $5$ by $4$ .

$\frac{20 - x \cdot 4 - 3 x}{4 x} = \frac{7}{x}$

Step 1.5.3

Multiply $4$ by $- 1$ .

$\frac{20 - 4 x - 3 x}{4 x} = \frac{7}{x}$

Step 1.5.4

Subtract $3 x$ from $- 4 x$ .

$\frac{20 - 7 x}{4 x} = \frac{7}{x}$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = - \frac{8}{7}$

Step 3