Linear Algebra Examples

$\frac{9}{2} x - \frac{1}{2} = \frac{71}{2}$

Step 1

Combine $\frac{9}{2}$ and $x$ .

$\frac{9 x}{2} - \frac{1}{2} = \frac{71}{2}$

Step 2

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

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Step 2.1

Add $\frac{1}{2}$ to both sides of the equation.

$\frac{9 x}{2} = \frac{71}{2} + \frac{1}{2}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{9 x}{2} = \frac{71 + 1}{2}$

Step 2.3

Add $71$ and $1$ .

$\frac{9 x}{2} = \frac{72}{2}$

Step 2.4

Divide $72$ by $2$ .

$\frac{9 x}{2} = 36$

Step 3

Multiply both sides of the equation by $\frac{2}{9}$ .

$\frac{2}{9} \cdot \frac{9 x}{2} = \frac{2}{9} \cdot 36$

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 $\frac{2}{9} \cdot \frac{9 x}{2}$ .

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{2}{9} \cdot \frac{9 x}{2} = \frac{2}{9} \cdot 36$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 x) = \frac{2}{9} \cdot 36$

Step 4.1.1.2

Cancel the common factor of $9$ .

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Step 4.1.1.2.1

Factor $9$ out of $9 x$ .

$\frac{1}{9} (9 (x)) = \frac{2}{9} \cdot 36$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 x) = \frac{2}{9} \cdot 36$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{2}{9} \cdot 36$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{2}{9} \cdot 36$ .

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Step 4.2.1.1

Cancel the common factor of $9$ .

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Step 4.2.1.1.1

Factor $9$ out of $36$ .

$x = \frac{2}{9} \cdot (9 (4))$

Step 4.2.1.1.2

Cancel the common factor.

$x = \frac{2}{9} \cdot (9 \cdot 4)$

Step 4.2.1.1.3

Rewrite the expression.

$x = 2 \cdot 4$

Step 4.2.1.2

Multiply $2$ by $4$ .

$x = 8$

Step 5

The domain is the set of all valid $x$ values.

${x | x = 8}$

Step 6