Algebra Examples

$2 \frac{3}{4} x = \frac{33}{2}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $2 \frac{3}{4} x$ .

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Step 1.1.1

Convert $2 \frac{3}{4}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$(2 + \frac{3}{4}) x = \frac{33}{2}$

Step 1.1.1.2

Add $2$ and $\frac{3}{4}$ .

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Step 1.1.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(2 \cdot \frac{4}{4} + \frac{3}{4}) x = \frac{33}{2}$

Step 1.1.1.2.2

Combine $2$ and $\frac{4}{4}$ .

$(\frac{2 \cdot 4}{4} + \frac{3}{4}) x = \frac{33}{2}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 3}{4} x = \frac{33}{2}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $4$ .

$\frac{8 + 3}{4} x = \frac{33}{2}$

Step 1.1.1.2.4.2

Add $8$ and $3$ .

$\frac{11}{4} x = \frac{33}{2}$

Step 1.1.2

Combine $\frac{11}{4}$ and $x$ .

$\frac{11 x}{4} = \frac{33}{2}$

Step 2

Multiply both sides of the equation by $\frac{4}{11}$ .

$\frac{4}{11} \cdot \frac{11 x}{4} = \frac{4}{11} \cdot \frac{33}{2}$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{4}{11} \cdot \frac{11 x}{4}$ .

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Step 3.1.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{4}{11} \cdot \frac{11 x}{4} = \frac{4}{11} \cdot \frac{33}{2}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{11} (11 x) = \frac{4}{11} \cdot \frac{33}{2}$

Step 3.1.1.2

Cancel the common factor of $11$ .

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Step 3.1.1.2.1

Factor $11$ out of $11 x$ .

$\frac{1}{11} (11 (x)) = \frac{4}{11} \cdot \frac{33}{2}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{11} (11 x) = \frac{4}{11} \cdot \frac{33}{2}$

Step 3.1.1.2.3

Rewrite the expression.

$x = \frac{4}{11} \cdot \frac{33}{2}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\frac{4}{11} \cdot \frac{33}{2}$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Factor $2$ out of $4$ .

$x = \frac{2 (2)}{11} \cdot \frac{33}{2}$

Step 3.2.1.1.2

Cancel the common factor.

$x = \frac{2 \cdot 2}{11} \cdot \frac{33}{2}$

Step 3.2.1.1.3

Rewrite the expression.

$x = \frac{2}{11} \cdot 33$

Step 3.2.1.2

Cancel the common factor of $11$ .

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Step 3.2.1.2.1

Factor $11$ out of $33$ .

$x = \frac{2}{11} \cdot (11 (3))$

Step 3.2.1.2.2

Cancel the common factor.

$x = \frac{2}{11} \cdot (11 \cdot 3)$

Step 3.2.1.2.3

Rewrite the expression.

$x = 2 \cdot 3$

Step 3.2.1.3

Multiply $2$ by $3$ .

$x = 6$