Solve by Factoring 3=1/4-5/x

$3 = \frac{1}{4} - \frac{5}{x}$

Step 1

Move all the expressions to the left side of the equation.

Subtract $\frac{1}{4}$ from both sides of the equation.

$3 - \frac{1}{4} = - \frac{5}{x}$

Add $\frac{5}{x}$ to both sides of the equation.

$3 - \frac{1}{4} + \frac{5}{x} = 0$

Step 2

Simplify $3 - \frac{1}{4} + \frac{5}{x}$ .

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

$3 \cdot \frac{4}{4} - \frac{1}{4} + \frac{5}{x} = 0$

Combine $3$ and $\frac{4}{4}$ .

$\frac{3 \cdot 4}{4} - \frac{1}{4} + \frac{5}{x} = 0$

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 - 1}{4} + \frac{5}{x} = 0$

Simplify the numerator.

Multiply $3$ by $4$ .

$\frac{12 - 1}{4} + \frac{5}{x} = 0$

Subtract $1$ from $12$ .

$\frac{11}{4} + \frac{5}{x} = 0$

Step 3

To write $\frac{11}{4}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{11}{4} \cdot \frac{x}{x} + \frac{5}{x} = 0$

Step 4

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

$\frac{11}{4} \cdot \frac{x}{x} + \frac{5}{x} \cdot \frac{4}{4} = 0$

Step 5

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

Multiply $\frac{11}{4}$ by $\frac{x}{x}$ .

$\frac{11 x}{4 x} + \frac{5}{x} \cdot \frac{4}{4} = 0$

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

$\frac{11 x}{4 x} + \frac{5 \cdot 4}{x \cdot 4} = 0$

Reorder the factors of $x \cdot 4$ .

$\frac{11 x}{4 x} + \frac{5 \cdot 4}{4 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{11 x + 5 \cdot 4}{4 x} = 0$

Step 7

Multiply $5$ by $4$ .

$\frac{11 x + 20}{4 x} = 0$

Step 8

Set the numerator equal to zero.

$11 x + 20 = 0$

Step 9

Solve the equation for $x$ .

Subtract $20$ from both sides of the equation.

$11 x = - 20$

Divide each term in $11 x = - 20$ by $11$ and simplify.

Divide each term in $11 x = - 20$ by $11$ .

$\frac{11 x}{11} = \frac{- 20}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{- 20}{11}$

Divide $x$ by $1$ .

$x = \frac{- 20}{11}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{20}{11}$

Solve by Factoring 3=1/4-5/x

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