Solve for x 1/2x-1/3(x-9)=3x

$\frac{1}{2} x - \frac{1}{3} (x - 9) = 3 x$

Step 1

Simplify $\frac{1}{2} x - \frac{1}{3} \cdot (x - 9)$ .

Simplify each term.

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} - \frac{1}{3} \cdot (x - 9) = 3 x$

Apply the distributive property.

$\frac{x}{2} - \frac{1}{3} x - \frac{1}{3} \cdot - 9 = 3 x$

Combine $x$ and $\frac{1}{3}$ .

$\frac{x}{2} - \frac{x}{3} - \frac{1}{3} \cdot - 9 = 3 x$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$\frac{x}{2} - \frac{x}{3} + \frac{- 1}{3} \cdot - 9 = 3 x$

Factor $3$ out of $- 9$ .

$\frac{x}{2} - \frac{x}{3} + \frac{- 1}{3} \cdot (3 (- 3)) = 3 x$

Cancel the common factor.

$\frac{x}{2} - \frac{x}{3} + \frac{- 1}{3} \cdot (3 \cdot - 3) = 3 x$

Rewrite the expression.

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

Multiply $- 1$ by $- 3$ .

$\frac{x}{2} - \frac{x}{3} + 3 = 3 x$

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

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

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

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

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

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

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

Multiply $2$ by $3$ .

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

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

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

Multiply $3$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x \cdot 3 - x \cdot 2$ .

Factor $x$ out of $x \cdot 3$ .

$\frac{x (3) - x \cdot 2}{6} + 3 = 3 x$

Factor $x$ out of $- x \cdot 2$ .

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

Factor $x$ out of $x (3) + x (- 1 \cdot 2)$ .

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

Multiply $- 1$ by $2$ .

$\frac{x (3 - 2)}{6} + 3 = 3 x$

Subtract $2$ from $3$ .

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

Multiply $x$ by $1$ .

$\frac{x}{6} + 3 = 3 x$

Step 2

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

Subtract $3 x$ from both sides of the equation.

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

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

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

Combine $- 3 x$ and $\frac{6}{6}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $x - 3 x \cdot 6$ .

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

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

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

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

Factor $x$ out of $- 3 x \cdot 6$ .

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

Factor $x$ out of $x \cdot 1 + x (- 3 \cdot 6)$ .

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

Multiply $- 3$ by $6$ .

$\frac{x (1 - 18)}{6} + 3 = 0$

Subtract $18$ from $1$ .

$\frac{x \cdot - 17}{6} + 3 = 0$

Move $- 17$ to the left of $x$ .

$\frac{- 17 \cdot x}{6} + 3 = 0$

Move the negative in front of the fraction.

$- \frac{17 x}{6} + 3 = 0$

Step 3

Subtract $3$ from both sides of the equation.

$- \frac{17 x}{6} = - 3$

Step 4

Multiply both sides of the equation by $- \frac{6}{17}$ .

$- \frac{6}{17} (- \frac{17 x}{6}) = - \frac{6}{17} \cdot - 3$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{6}{17} (- \frac{17 x}{6})$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{6}{17}$ into the numerator.

$\frac{- 6}{17} (- \frac{17 x}{6}) = - \frac{6}{17} \cdot - 3$

Move the leading negative in $- \frac{17 x}{6}$ into the numerator.

$\frac{- 6}{17} \cdot \frac{- 17 x}{6} = - \frac{6}{17} \cdot - 3$

Factor $6$ out of $- 6$ .

$\frac{6 (- 1)}{17} \cdot \frac{- 17 x}{6} = - \frac{6}{17} \cdot - 3$

Cancel the common factor.

$\frac{6 \cdot - 1}{17} \cdot \frac{- 17 x}{6} = - \frac{6}{17} \cdot - 3$

Rewrite the expression.

$\frac{- 1}{17} (- 17 x) = - \frac{6}{17} \cdot - 3$

Cancel the common factor of $17$ .

Factor $17$ out of $- 17 x$ .

$\frac{- 1}{17} (17 (- x)) = - \frac{6}{17} \cdot - 3$

Cancel the common factor.

$\frac{- 1}{17} (17 (- x)) = - \frac{6}{17} \cdot - 3$

Rewrite the expression.

$- - x = - \frac{6}{17} \cdot - 3$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{6}{17} \cdot - 3$

Multiply $x$ by $1$ .

$x = - \frac{6}{17} \cdot - 3$

Simplify the right side.

Multiply $- \frac{6}{17} \cdot - 3$ .

Multiply $- 3$ by $- 1$ .

$x = 3 (\frac{6}{17})$

Combine $3$ and $\frac{6}{17}$ .

$x = \frac{3 \cdot 6}{17}$

Multiply $3$ by $6$ .

$x = \frac{18}{17}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{18}{17}$

Decimal Form:

$x = 1.05882352 \dots$

Mixed Number Form:

$x = 1 \frac{1}{17}$

Solve for x 1/2x-1/3(x-9)=3x

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