Solve by Factoring 1/8+1/6=1/x

$\frac{1}{8} + \frac{1}{6} = \frac{1}{x}$

Step 1

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

$\frac{1}{8} + \frac{1}{6} - \frac{1}{x} = 0$

Step 2

Simplify $\frac{1}{8} + \frac{1}{6} - \frac{1}{x}$ .

To write $\frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{8} \cdot \frac{3}{3} + \frac{1}{6} - \frac{1}{x} = 0$

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{8} \cdot \frac{3}{3} + \frac{1}{6} \cdot \frac{4}{4} - \frac{1}{x} = 0$

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{8}$ by $\frac{3}{3}$ .

$\frac{3}{8 \cdot 3} + \frac{1}{6} \cdot \frac{4}{4} - \frac{1}{x} = 0$

Multiply $8$ by $3$ .

$\frac{3}{24} + \frac{1}{6} \cdot \frac{4}{4} - \frac{1}{x} = 0$

Multiply $\frac{1}{6}$ by $\frac{4}{4}$ .

$\frac{3}{24} + \frac{4}{6 \cdot 4} - \frac{1}{x} = 0$

Multiply $6$ by $4$ .

$\frac{3}{24} + \frac{4}{24} - \frac{1}{x} = 0$

Combine the numerators over the common denominator.

$\frac{3 + 4}{24} - \frac{1}{x} = 0$

Add $3$ and $4$ .

$\frac{7}{24} - \frac{1}{x} = 0$

Step 3

To write $\frac{7}{24}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$\frac{7}{24} \cdot \frac{x}{x} - \frac{1}{x} = 0$

Step 4

To write $- \frac{1}{x}$ as a fraction with a common denominator, multiply by $\frac{24}{24}$ .

$\frac{7}{24} \cdot \frac{x}{x} - \frac{1}{x} \cdot \frac{24}{24} = 0$

Step 5

Write each expression with a common denominator of $24 x$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{7}{24}$ by $\frac{x}{x}$ .

$\frac{7 x}{24 x} - \frac{1}{x} \cdot \frac{24}{24} = 0$

Multiply $\frac{1}{x}$ by $\frac{24}{24}$ .

$\frac{7 x}{24 x} - \frac{24}{x \cdot 24} = 0$

Reorder the factors of $x \cdot 24$ .

$\frac{7 x}{24 x} - \frac{24}{24 x} = 0$

Step 6

Combine the numerators over the common denominator.

$\frac{7 x - 24}{24 x} = 0$

Step 7

Set the numerator equal to zero.

$7 x - 24 = 0$

Step 8

Solve the equation for $x$ .

Add $24$ to both sides of the equation.

$7 x = 24$

Divide each term in $7 x = 24$ by $7$ and simplify.

Divide each term in $7 x = 24$ by $7$ .

$\frac{7 x}{7} = \frac{24}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{24}{7}$

Divide $x$ by $1$ .

$x = \frac{24}{7}$

Solve by Factoring 1/8+1/6=1/x

Related Questions

Support LCMGCF.com by disabling your adblocker.