Algebra Examples

$4 \frac{6}{8} + 2 \frac{1}{2} - x = 0$

Step 1

Simplify the left side.

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Step 1.1

Simplify $4 \frac{6}{8} + 2 \frac{1}{2} - x$ .

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Step 1.1.1

Convert $4 \frac{6}{8}$ 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.

$4 + \frac{6}{8} + 2 \frac{1}{2} - x = 0$

Step 1.1.1.2

Add $4$ and $\frac{6}{8}$ .

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Step 1.1.1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$4 \cdot \frac{8}{8} + \frac{6}{8} + 2 \frac{1}{2} - x = 0$

Step 1.1.1.2.2

Combine $4$ and $\frac{8}{8}$ .

$\frac{4 \cdot 8}{8} + \frac{6}{8} + 2 \frac{1}{2} - x = 0$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 8 + 6}{8} + 2 \frac{1}{2} - x = 0$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $4$ by $8$ .

$\frac{32 + 6}{8} + 2 \frac{1}{2} - x = 0$

Step 1.1.1.2.4.2

Add $32$ and $6$ .

$\frac{38}{8} + 2 \frac{1}{2} - x = 0$

Step 1.1.2

Convert $2 \frac{1}{2}$ to an improper fraction.

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Step 1.1.2.1

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

$\frac{38}{8} + 2 + \frac{1}{2} - x = 0$

Step 1.1.2.2

Add $2$ and $\frac{1}{2}$ .

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Step 1.1.2.2.1

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

$\frac{38}{8} + 2 \cdot \frac{2}{2} + \frac{1}{2} - x = 0$

Step 1.1.2.2.2

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

$\frac{38}{8} + \frac{2 \cdot 2}{2} + \frac{1}{2} - x = 0$

Step 1.1.2.2.3

Combine the numerators over the common denominator.

$\frac{38}{8} + \frac{2 \cdot 2 + 1}{2} - x = 0$

Step 1.1.2.2.4

Simplify the numerator.

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Step 1.1.2.2.4.1

Multiply $2$ by $2$ .

$\frac{38}{8} + \frac{4 + 1}{2} - x = 0$

Step 1.1.2.2.4.2

Add $4$ and $1$ .

$\frac{38}{8} + \frac{5}{2} - x = 0$

Step 1.1.3

Cancel the common factor of $38$ and $8$ .

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Step 1.1.3.1

Factor $2$ out of $38$ .

$\frac{2 (19)}{8} + \frac{5}{2} - x = 0$

Step 1.1.3.2

Cancel the common factors.

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Step 1.1.3.2.1

Factor $2$ out of $8$ .

$\frac{2 \cdot 19}{2 \cdot 4} + \frac{5}{2} - x = 0$

Step 1.1.3.2.2

Cancel the common factor.

$\frac{2 \cdot 19}{2 \cdot 4} + \frac{5}{2} - x = 0$

Step 1.1.3.2.3

Rewrite the expression.

$\frac{19}{4} + \frac{5}{2} - x = 0$

Step 1.1.4

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{19}{4} + \frac{5}{2} \cdot \frac{2}{2} - x = 0$

Step 1.1.5

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.1.5.1

Multiply $\frac{5}{2}$ by $\frac{2}{2}$ .

$\frac{19}{4} + \frac{5 \cdot 2}{2 \cdot 2} - x = 0$

Step 1.1.5.2

Multiply $2$ by $2$ .

$\frac{19}{4} + \frac{5 \cdot 2}{4} - x = 0$

Step 1.1.6

Combine the numerators over the common denominator.

$\frac{19 + 5 \cdot 2}{4} - x = 0$

Step 1.1.7

Simplify the numerator.

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Step 1.1.7.1

Multiply $5$ by $2$ .

$\frac{19 + 10}{4} - x = 0$

Step 1.1.7.2

Add $19$ and $10$ .

$\frac{29}{4} - x = 0$

Step 2

Subtract $\frac{29}{4}$ from both sides of the equation.

$- x = - \frac{29}{4}$

Step 3

Divide each term in $- x = - \frac{29}{4}$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- x = - \frac{29}{4}$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- \frac{29}{4}}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- \frac{29}{4}}{- 1}$

Step 3.2.2

Divide $x$ by $1$ .

$x = \frac{- \frac{29}{4}}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Dividing two negative values results in a positive value.

$x = \frac{\frac{29}{4}}{1}$

Step 3.3.2

Divide $\frac{29}{4}$ by $1$ .

$x = \frac{29}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{29}{4}$

Decimal Form:

$x = 7.25$

Mixed Number Form:

$x = 7 \frac{1}{4}$