Solve by Factoring 1/2+6/x=5/6

$\frac{1}{2} + \frac{6}{x} = \frac{5}{6}$

Step 1

Subtract $\frac{5}{6}$ from both sides of the equation.

$\frac{1}{2} + \frac{6}{x} - \frac{5}{6} = 0$

Step 2

Simplify $\frac{1}{2} + \frac{6}{x} - \frac{5}{6}$ .

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{6}{x} + \frac{1}{2} \cdot \frac{3}{3} - \frac{5}{6} = 0$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{6}{x} + \frac{3}{2 \cdot 3} - \frac{5}{6} = 0$

Multiply $2$ by $3$ .

$\frac{6}{x} + \frac{3}{6} - \frac{5}{6} = 0$

Combine the numerators over the common denominator.

$\frac{6}{x} + \frac{3 - 5}{6} = 0$

Subtract $5$ from $3$ .

$\frac{6}{x} + \frac{- 2}{6} = 0$

Simplify each term.

Cancel the common factor of $- 2$ and $6$ .

Factor $2$ out of $- 2$ .

$\frac{6}{x} + \frac{2 (- 1)}{6} = 0$

Cancel the common factors.

Factor $2$ out of $6$ .

$\frac{6}{x} + \frac{2 \cdot - 1}{2 \cdot 3} = 0$

Cancel the common factor.

$\frac{6}{x} + \frac{2 \cdot - 1}{2 \cdot 3} = 0$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 3

To write $\frac{6}{x}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 4

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

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

Step 5

Write each expression with a common denominator of $x \cdot 3$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{6}{x}$ by $\frac{3}{3}$ .

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

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

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

Reorder the factors of $x \cdot 3$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Multiply $6$ by $3$ .

$\frac{18 - x}{3 x} = 0$

Step 8

Set the numerator equal to zero.

$18 - x = 0$

Step 9

Solve the equation for $x$ .

Subtract $18$ from both sides of the equation.

$- x = - 18$

Divide each term in $- x = - 18$ by $- 1$ and simplify.

Divide each term in $- x = - 18$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 18}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 18}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 18}{- 1}$

Simplify the right side.

Divide $- 18$ by $- 1$ .

$x = 18$

Solve by Factoring 1/2+6/x=5/6

Related Questions

Support LCMGCF.com by disabling your adblocker.