Finite Math Examples

$\frac{1}{4} \cdot (x + 4) = x$

Step 1

Simplify $\frac{1}{4} \cdot (x + 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{4} \cdot (x + 4) = x$

Step 1.2

Simplify by adding zeros.

$\frac{1}{4} \cdot (x + 4) = x$

Step 1.3

Apply the distributive property.

$\frac{1}{4} x + \frac{1}{4} \cdot 4 = x$

Step 1.4

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} + \frac{1}{4} \cdot 4 = x$

Step 1.5

Cancel the common factor of $4$ .

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Step 1.5.1

Cancel the common factor.

$\frac{x}{4} + \frac{1}{4} \cdot 4 = x$

Step 1.5.2

Rewrite the expression.

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

Step 2

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

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Step 2.1

Subtract $x$ from both sides of the equation.

$\frac{x}{4} + 1 - x = 0$

Step 2.2

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

$\frac{x}{4} - x \cdot \frac{4}{4} + 1 = 0$

Step 2.3

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

$\frac{x}{4} + \frac{- x \cdot 4}{4} + 1 = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{x - x \cdot 4}{4} + 1 = 0$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $x$ out of $x - x \cdot 4$ .

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Step 2.5.1.1.1

Raise $x$ to the power of $1$ .

$\frac{x^{1} - x \cdot 4}{4} + 1 = 0$

Step 2.5.1.1.2

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - x \cdot 4}{4} + 1 = 0$

Step 2.5.1.1.3

Factor $x$ out of $- x \cdot 4$ .

$\frac{x \cdot 1 + x (- 1 \cdot 4)}{4} + 1 = 0$

Step 2.5.1.1.4

Factor $x$ out of $x \cdot 1 + x (- 1 \cdot 4)$ .

$\frac{x (1 - 1 \cdot 4)}{4} + 1 = 0$

Step 2.5.1.2

Multiply $- 1$ by $4$ .

$\frac{x (1 - 4)}{4} + 1 = 0$

Step 2.5.1.3

Subtract $4$ from $1$ .

$\frac{x \cdot - 3}{4} + 1 = 0$

Step 2.5.2

Move $- 3$ to the left of $x$ .

$\frac{- 3 \cdot x}{4} + 1 = 0$

Step 2.5.3

Move the negative in front of the fraction.

$- \frac{3 x}{4} + 1 = 0$

Step 3

Subtract $1$ from both sides of the equation.

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

Step 4

Multiply both sides of the equation by $- \frac{4}{3}$ .

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

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{4}{3} (- \frac{3 x}{4})$ .

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Step 5.1.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

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

Step 5.1.1.1.2

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

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

Step 5.1.1.1.3

Factor $4$ out of $- 4$ .

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

Step 5.1.1.1.4

Cancel the common factor.

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

Step 5.1.1.1.5

Rewrite the expression.

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

Step 5.1.1.2

Cancel the common factor of $3$ .

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Step 5.1.1.2.1

Factor $3$ out of $- 3 x$ .

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

Step 5.1.1.2.2

Cancel the common factor.

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

Step 5.1.1.2.3

Rewrite the expression.

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

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 5.1.1.3.2

Multiply $x$ by $1$ .

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

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- \frac{4}{3} \cdot - 1$ .

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Step 5.2.1.1

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{4}{3})$

Step 5.2.1.2

Multiply $\frac{4}{3}$ by $1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.\overline{3}$

Mixed Number Form:

$x = 1 \frac{1}{3}$