Solve by Factoring 5/(3x)+1=7/6

$\frac{5}{3 x} + 1 = \frac{7}{6}$

Step 1

Subtract $\frac{7}{6}$ from both sides of the equation.

$\frac{5}{3 x} + 1 - \frac{7}{6} = 0$

Step 2

Simplify $\frac{5}{3 x} + 1 - \frac{7}{6}$ .

Write $1$ as a fraction with a common denominator.

$\frac{5}{3 x} + \frac{6}{6} - \frac{7}{6} = 0$

Combine the numerators over the common denominator.

$\frac{5}{3 x} + \frac{6 - 7}{6} = 0$

Subtract $7$ from $6$ .

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

Move the negative in front of the fraction.

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

Step 3

To write $\frac{5}{3 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4

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

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

Step 5

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

Multiply $\frac{5}{3 x}$ by $\frac{2}{2}$ .

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

Multiply $2$ by $3$ .

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

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

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Multiply $5$ by $2$ .

$\frac{10 - x}{6 x} = 0$

Step 8

Set the numerator equal to zero.

$10 - x = 0$

Step 9

Solve the equation for $x$ .

Subtract $10$ from both sides of the equation.

$- x = - 10$

Divide each term in $- x = - 10$ by $- 1$ and simplify.

Divide each term in $- x = - 10$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 10}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 10}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 10}{- 1}$

Simplify the right side.

Divide $- 10$ by $- 1$ .

$x = 10$

Solve by Factoring 5/(3x)+1=7/6

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