Pre-Algebra Examples

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

Step 1

Multiply both sides by $2$ .

$\frac{2 x - 3}{2} \cdot 2 = \frac{3}{4} \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{2 x - 3}{2} \cdot 2 = \frac{3}{4} \cdot 2$

Step 2.1.1.2

Rewrite the expression.

$2 x - 3 = \frac{3}{4} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Factor $2$ out of $4$ .

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

Step 2.2.1.2

Cancel the common factor.

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

Step 2.2.1.3

Rewrite the expression.

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

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Add $3$ to both sides of the equation.

$2 x = \frac{3}{2} + 3$

Step 3.1.2

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

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

Step 3.1.3

Combine $3$ and $\frac{2}{2}$ .

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

Step 3.1.4

Combine the numerators over the common denominator.

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

Step 3.1.5

Simplify the numerator.

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Step 3.1.5.1

Multiply $3$ by $2$ .

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

Step 3.1.5.2

Add $3$ and $6$ .

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

Step 3.2

Divide each term in $2 x = \frac{9}{2}$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 x = \frac{9}{2}$ by $2$ .

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

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

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

Step 3.2.2.1.2

Divide $x$ by $1$ .

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

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{9}{2} \cdot \frac{1}{2}$

Step 3.2.3.2

Multiply $\frac{9}{2} \cdot \frac{1}{2}$ .

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Step 3.2.3.2.1

Multiply $\frac{9}{2}$ by $\frac{1}{2}$ .

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

Step 3.2.3.2.2

Multiply $2$ by $2$ .

$x = \frac{9}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9}{4}$

Decimal Form:

$x = 2.25$

Mixed Number Form:

$x = 2 \frac{1}{4}$