Algebra Examples

$\frac{x}{3} - \frac{1}{4} = \frac{1}{3} - \frac{x}{4}$

Step 1

Multiply each term in $\frac{x}{3} - \frac{1}{4} = \frac{1}{3} - \frac{x}{4}$ by $12$ to eliminate the fractions.

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Step 1.1

Multiply each term in $\frac{x}{3} - \frac{1}{4} = \frac{1}{3} - \frac{x}{4}$ by $12$ .

$\frac{x}{3} \cdot 12 - \frac{1}{4} \cdot 12 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Cancel the common factor of $3$ .

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Step 1.2.1.1.1

Factor $3$ out of $12$ .

$\frac{x}{3} \cdot (3 (4)) - \frac{1}{4} \cdot 12 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Step 1.2.1.1.2

Cancel the common factor.

$\frac{x}{3} \cdot (3 \cdot 4) - \frac{1}{4} \cdot 12 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Step 1.2.1.1.3

Rewrite the expression.

$x \cdot 4 - \frac{1}{4} \cdot 12 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Step 1.2.1.2

Move $4$ to the left of $x$ .

$4 \cdot x - \frac{1}{4} \cdot 12 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Step 1.2.1.3

Cancel the common factor of $4$ .

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Step 1.2.1.3.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$4 x + \frac{- 1}{4} \cdot 12 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Step 1.2.1.3.2

Factor $4$ out of $12$ .

$4 x + \frac{- 1}{4} \cdot (4 (3)) = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Step 1.2.1.3.3

Cancel the common factor.

$4 x + \frac{- 1}{4} \cdot (4 \cdot 3) = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Step 1.2.1.3.4

Rewrite the expression.

$4 x - 1 \cdot 3 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Step 1.2.1.4

Multiply $- 1$ by $3$ .

$4 x - 3 = \frac{1}{3} \cdot 12 - \frac{x}{4} \cdot 12$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Cancel the common factor of $3$ .

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Step 1.3.1.1.1

Factor $3$ out of $12$ .

$4 x - 3 = \frac{1}{3} \cdot (3 (4)) - \frac{x}{4} \cdot 12$

Step 1.3.1.1.2

Cancel the common factor.

$4 x - 3 = \frac{1}{3} \cdot (3 \cdot 4) - \frac{x}{4} \cdot 12$

Step 1.3.1.1.3

Rewrite the expression.

$4 x - 3 = 4 - \frac{x}{4} \cdot 12$

Step 1.3.1.2

Cancel the common factor of $4$ .

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Step 1.3.1.2.1

Move the leading negative in $- \frac{x}{4}$ into the numerator.

$4 x - 3 = 4 + \frac{- x}{4} \cdot 12$

Step 1.3.1.2.2

Factor $4$ out of $12$ .

$4 x - 3 = 4 + \frac{- x}{4} \cdot (4 (3))$

Step 1.3.1.2.3

Cancel the common factor.

$4 x - 3 = 4 + \frac{- x}{4} \cdot (4 \cdot 3)$

Step 1.3.1.2.4

Rewrite the expression.

$4 x - 3 = 4 - x \cdot 3$

Step 1.3.1.3

Multiply $3$ by $- 1$ .

$4 x - 3 = 4 - 3 x$

Step 2

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

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Step 2.1

Add $3 x$ to both sides of the equation.

$4 x - 3 + 3 x = 4$

Step 2.2

Add $4 x$ and $3 x$ .

$7 x - 3 = 4$

Step 3

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

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Step 3.1

Add $3$ to both sides of the equation.

$7 x = 4 + 3$

Step 3.2

Add $4$ and $3$ .

$7 x = 7$

Step 4

Divide each term in $7 x = 7$ by $7$ and simplify.

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Step 4.1

Divide each term in $7 x = 7$ by $7$ .

$\frac{7 x}{7} = \frac{7}{7}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $7$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{7}{7}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{7}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $7$ by $7$ .

$x = 1$