Precalculus Examples Polynomial and Rational Functions

Solve for x

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

Step 1

Cancel the common factor of $3$ and $6$ .

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Step 1.1

Factor $3$ out of $3 x$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $6$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Subtract $\frac{1}{3}$ from both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Multiply $3$ by $2$ .

$- \frac{x}{2} = - \frac{1}{6} - \frac{2}{6}$

Step 2.4

Combine the numerators over the common denominator.

$- \frac{x}{2} = \frac{- 1 - 2}{6}$

Step 2.5

Subtract $2$ from $- 1$ .

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

Step 2.6

Cancel the common factor of $- 3$ and $6$ .

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Step 2.6.1

Factor $3$ out of $- 3$ .

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

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $3$ out of $6$ .

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

Step 2.6.2.2

Cancel the common factor.

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

Step 2.6.2.3

Rewrite the expression.

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

Step 2.7

Move the negative in front of the fraction.

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

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- x = - 1$

Step 4

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

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Step 4.1

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

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

Step 4.2.2

Divide $x$ by $1$ .

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

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 1$ by $- 1$ .

$x = 1$

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