Solve for x 1/5x-1/6(x-5)=6x

$\frac{1}{5} x - \frac{1}{6} (x - 5) = 6 x$

Step 1

Simplify $\frac{1}{5} x - \frac{1}{6} \cdot (x - 5)$ .

Simplify each term.

Combine $\frac{1}{5}$ and $x$ .

$\frac{x}{5} - \frac{1}{6} \cdot (x - 5) = 6 x$

Apply the distributive property.

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

Combine $x$ and $\frac{1}{6}$ .

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

Multiply $- \frac{1}{6} \cdot - 5$ .

Multiply $- 5$ by $- 1$ .

$\frac{x}{5} - \frac{x}{6} + 5 (\frac{1}{6}) = 6 x$

Combine $5$ and $\frac{1}{6}$ .

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

To write $\frac{x}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

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

To write $- \frac{x}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{5}$ by $\frac{6}{6}$ .

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

Multiply $5$ by $6$ .

$\frac{x \cdot 6}{30} - \frac{x}{6} \cdot \frac{5}{5} + \frac{5}{6} = 6 x$

Multiply $\frac{x}{6}$ by $\frac{5}{5}$ .

$\frac{x \cdot 6}{30} - \frac{x \cdot 5}{6 \cdot 5} + \frac{5}{6} = 6 x$

Multiply $6$ by $5$ .

$\frac{x \cdot 6}{30} - \frac{x \cdot 5}{30} + \frac{5}{6} = 6 x$

Combine the numerators over the common denominator.

$\frac{x \cdot 6 - x \cdot 5}{30} + \frac{5}{6} = 6 x$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x \cdot 6 - x \cdot 5$ .

Factor $x$ out of $x \cdot 6$ .

$\frac{x (6) - x \cdot 5}{30} + \frac{5}{6} = 6 x$

Factor $x$ out of $- x \cdot 5$ .

$\frac{x (6) + x (- 1 \cdot 5)}{30} + \frac{5}{6} = 6 x$

Factor $x$ out of $x (6) + x (- 1 \cdot 5)$ .

$\frac{x (6 - 1 \cdot 5)}{30} + \frac{5}{6} = 6 x$

Multiply $- 1$ by $5$ .

$\frac{x (6 - 5)}{30} + \frac{5}{6} = 6 x$

Subtract $5$ from $6$ .

$\frac{x \cdot 1}{30} + \frac{5}{6} = 6 x$

Multiply $x$ by $1$ .

$\frac{x}{30} + \frac{5}{6} = 6 x$

Step 2

Move all terms containing $x$ to the left side of the equation.

Subtract $6 x$ from both sides of the equation.

$\frac{x}{30} + \frac{5}{6} - 6 x = 0$

To write $- 6 x$ as a fraction with a common denominator, multiply by $\frac{30}{30}$ .

$\frac{x}{30} - 6 x \cdot \frac{30}{30} + \frac{5}{6} = 0$

Combine $- 6 x$ and $\frac{30}{30}$ .

$\frac{x}{30} + \frac{- 6 x \cdot 30}{30} + \frac{5}{6} = 0$

Combine the numerators over the common denominator.

$\frac{x - 6 x \cdot 30}{30} + \frac{5}{6} = 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x - 6 x \cdot 30$ .

Raise $x$ to the power of $1$ .

$\frac{x^{1} - 6 x \cdot 30}{30} + \frac{5}{6} = 0$

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - 6 x \cdot 30}{30} + \frac{5}{6} = 0$

Factor $x$ out of $- 6 x \cdot 30$ .

$\frac{x \cdot 1 + x (- 6 \cdot 30)}{30} + \frac{5}{6} = 0$

Factor $x$ out of $x \cdot 1 + x (- 6 \cdot 30)$ .

$\frac{x (1 - 6 \cdot 30)}{30} + \frac{5}{6} = 0$

Multiply $- 6$ by $30$ .

$\frac{x (1 - 180)}{30} + \frac{5}{6} = 0$

Subtract $180$ from $1$ .

$\frac{x \cdot - 179}{30} + \frac{5}{6} = 0$

Move $- 179$ to the left of $x$ .

$\frac{- 179 \cdot x}{30} + \frac{5}{6} = 0$

Move the negative in front of the fraction.

$- \frac{179 x}{30} + \frac{5}{6} = 0$

Step 3

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

$- \frac{179 x}{30} = - \frac{5}{6}$

Step 4

Multiply both sides of the equation by $- \frac{30}{179}$ .

$- \frac{30}{179} (- \frac{179 x}{30}) = - \frac{30}{179} (- \frac{5}{6})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{30}{179} (- \frac{179 x}{30})$ .

Cancel the common factor of $30$ .

Move the leading negative in $- \frac{30}{179}$ into the numerator.

$\frac{- 30}{179} (- \frac{179 x}{30}) = - \frac{30}{179} (- \frac{5}{6})$

Move the leading negative in $- \frac{179 x}{30}$ into the numerator.

$\frac{- 30}{179} \cdot \frac{- 179 x}{30} = - \frac{30}{179} (- \frac{5}{6})$

Factor $30$ out of $- 30$ .

$\frac{30 (- 1)}{179} \cdot \frac{- 179 x}{30} = - \frac{30}{179} (- \frac{5}{6})$

Cancel the common factor.

$\frac{30 \cdot - 1}{179} \cdot \frac{- 179 x}{30} = - \frac{30}{179} (- \frac{5}{6})$

Rewrite the expression.

$\frac{- 1}{179} (- 179 x) = - \frac{30}{179} (- \frac{5}{6})$

Cancel the common factor of $179$ .

Factor $179$ out of $- 179 x$ .

$\frac{- 1}{179} (179 (- x)) = - \frac{30}{179} (- \frac{5}{6})$

Cancel the common factor.

$\frac{- 1}{179} (179 (- x)) = - \frac{30}{179} (- \frac{5}{6})$

Rewrite the expression.

$- - x = - \frac{30}{179} (- \frac{5}{6})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{30}{179} (- \frac{5}{6})$

Multiply $x$ by $1$ .

$x = - \frac{30}{179} (- \frac{5}{6})$

Simplify the right side.

Simplify $- \frac{30}{179} (- \frac{5}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{30}{179}$ into the numerator.

$x = \frac{- 30}{179} (- \frac{5}{6})$

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$x = \frac{- 30}{179} \cdot \frac{- 5}{6}$

Factor $6$ out of $- 30$ .

$x = \frac{6 (- 5)}{179} \cdot \frac{- 5}{6}$

Cancel the common factor.

$x = \frac{6 \cdot - 5}{179} \cdot \frac{- 5}{6}$

Rewrite the expression.

$x = \frac{- 5}{179} \cdot - 5$

Combine $\frac{- 5}{179}$ and $- 5$ .

$x = \frac{- 5 \cdot - 5}{179}$

Multiply $- 5$ by $- 5$ .

$x = \frac{25}{179}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{25}{179}$

Decimal Form:

$x = 0.13966480 \dots$

Solve for x 1/5x-1/6(x-5)=6x

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