Finite Math Examples

$\frac{2 x - \frac{1}{2}}{4} = 3$

Step 1

Multiply both sides by $4$ .

$\frac{2 x - \frac{1}{2}}{4} \cdot 4 = 3 \cdot 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{2 x - \frac{1}{2}}{4} \cdot 4$ .

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Step 2.1.1.1

Simplify the numerator.

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Step 2.1.1.1.1

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

$\frac{2 x \cdot \frac{2}{2} - \frac{1}{2}}{4} \cdot 4 = 3 \cdot 4$

Step 2.1.1.1.2

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

$\frac{\frac{2 x \cdot 2}{2} - \frac{1}{2}}{4} \cdot 4 = 3 \cdot 4$

Step 2.1.1.1.3

Combine the numerators over the common denominator.

$\frac{\frac{2 x \cdot 2 - 1}{2}}{4} \cdot 4 = 3 \cdot 4$

Step 2.1.1.1.4

Multiply $2$ by $2$ .

$\frac{\frac{4 x - 1}{2}}{4} \cdot 4 = 3 \cdot 4$

Step 2.1.1.2

Cancel the common factor of $4$ .

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Step 2.1.1.2.1

Cancel the common factor.

$\frac{\frac{4 x - 1}{2}}{4} \cdot 4 = 3 \cdot 4$

Step 2.1.1.2.2

Rewrite the expression.

$\frac{4 x - 1}{2} = 3 \cdot 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $3$ by $4$ .

$\frac{4 x - 1}{2} = 12$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $2$ .

$\frac{4 x - 1}{2} \cdot 2 = 12 \cdot 2$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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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

Cancel the common factor.

$\frac{4 x - 1}{2} \cdot 2 = 12 \cdot 2$

Step 3.2.1.1.2

Rewrite the expression.

$4 x - 1 = 12 \cdot 2$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Multiply $12$ by $2$ .

$4 x - 1 = 24$

Step 3.3

Solve for $x$ .

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Step 3.3.1

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

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Step 3.3.1.1

Add $1$ to both sides of the equation.

$4 x = 24 + 1$

Step 3.3.1.2

Add $24$ and $1$ .

$4 x = 25$

Step 3.3.2

Divide each term in $4 x = 25$ by $4$ and simplify.

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Step 3.3.2.1

Divide each term in $4 x = 25$ by $4$ .

$\frac{4 x}{4} = \frac{25}{4}$

Step 3.3.2.2

Simplify the left side.

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Step 3.3.2.2.1

Cancel the common factor of $4$ .

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Step 3.3.2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{25}{4}$

Step 3.3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{25}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{25}{4}$

Decimal Form:

$x = 6.25$

Mixed Number Form:

$x = 6 \frac{1}{4}$