Linear Algebra Examples

$x - \frac{13}{12} = \frac{5 x}{18} + \frac{13}{12}$

Step 1

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

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Step 1.1

Subtract $\frac{5 x}{18}$ from both sides of the equation.

$x - \frac{13}{12} - \frac{5 x}{18} = \frac{13}{12}$

Step 1.2

To write $x$ as a fraction with a common denominator, multiply by $\frac{18}{18}$ .

$x \cdot \frac{18}{18} - \frac{5 x}{18} - \frac{13}{12} = \frac{13}{12}$

Step 1.3

Combine $x$ and $\frac{18}{18}$ .

$\frac{x \cdot 18}{18} - \frac{5 x}{18} - \frac{13}{12} = \frac{13}{12}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 18 - 5 x}{18} - \frac{13}{12} = \frac{13}{12}$

Step 1.5

Subtract $5 x$ from $x \cdot 18$ .

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Step 1.5.1

Reorder $x$ and $18$ .

$\frac{18 \cdot x - 5 x}{18} - \frac{13}{12} = \frac{13}{12}$

Step 1.5.2

Subtract $5 x$ from $18 \cdot x$ .

$\frac{13 \cdot x}{18} - \frac{13}{12} = \frac{13}{12}$

$\frac{13 x}{18} - \frac{13}{12} = \frac{13}{12}$

Step 2

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

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Step 2.1

Add $\frac{13}{12}$ to both sides of the equation.

$\frac{13 x}{18} = \frac{13}{12} + \frac{13}{12}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{13 x}{18} = \frac{13 + 13}{12}$

Step 2.3

Add $13$ and $13$ .

$\frac{13 x}{18} = \frac{26}{12}$

Step 2.4

Cancel the common factor of $26$ and $12$ .

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Step 2.4.1

Factor $2$ out of $26$ .

$\frac{13 x}{18} = \frac{2 (13)}{12}$

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $12$ .

$\frac{13 x}{18} = \frac{2 \cdot 13}{2 \cdot 6}$

Step 2.4.2.2

Cancel the common factor.

$\frac{13 x}{18} = \frac{2 \cdot 13}{2 \cdot 6}$

Step 2.4.2.3

Rewrite the expression.

$\frac{13 x}{18} = \frac{13}{6}$

Step 3

Multiply both sides of the equation by $\frac{18}{13}$ .

$\frac{18}{13} \cdot \frac{13 x}{18} = \frac{18}{13} \cdot \frac{13}{6}$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{18}{13} \cdot \frac{13 x}{18}$ .

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Step 4.1.1.1

Cancel the common factor of $18$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{18}{13} \cdot \frac{13 x}{18} = \frac{18}{13} \cdot \frac{13}{6}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{13} (13 x) = \frac{18}{13} \cdot \frac{13}{6}$

Step 4.1.1.2

Cancel the common factor of $13$ .

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Step 4.1.1.2.1

Factor $13$ out of $13 x$ .

$\frac{1}{13} (13 (x)) = \frac{18}{13} \cdot \frac{13}{6}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{13} (13 x) = \frac{18}{13} \cdot \frac{13}{6}$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{18}{13} \cdot \frac{13}{6}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{18}{13} \cdot \frac{13}{6}$ .

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Step 4.2.1.1

Cancel the common factor of $6$ .

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Step 4.2.1.1.1

Factor $6$ out of $18$ .

$x = \frac{6 (3)}{13} \cdot \frac{13}{6}$

Step 4.2.1.1.2

Cancel the common factor.

$x = \frac{6 \cdot 3}{13} \cdot \frac{13}{6}$

Step 4.2.1.1.3

Rewrite the expression.

$x = \frac{3}{13} \cdot 13$

Step 4.2.1.2

Cancel the common factor of $13$ .

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Step 4.2.1.2.1

Cancel the common factor.

$x = \frac{3}{13} \cdot 13$

Step 4.2.1.2.2

Rewrite the expression.

$x = 3$