Algebra Examples

$- 2 \frac{1}{2} + (- 5 \cdot x) = - 27 \frac{1}{2}$

Step 1

Simplify the left side.

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Step 1.1

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

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Step 1.1.1

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

$- (2 + \frac{1}{2}) - 5 \cdot x = - 27 \frac{1}{2}$

Step 1.1.2

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

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Step 1.1.2.1

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

$- (2 \cdot \frac{2}{2} + \frac{1}{2}) - 5 \cdot x = - 27 \frac{1}{2}$

Step 1.1.2.2

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

$- (\frac{2 \cdot 2}{2} + \frac{1}{2}) - 5 \cdot x = - 27 \frac{1}{2}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$- \frac{2 \cdot 2 + 1}{2} - 5 \cdot x = - 27 \frac{1}{2}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $2$ by $2$ .

$- \frac{4 + 1}{2} - 5 \cdot x = - 27 \frac{1}{2}$

Step 1.1.2.4.2

Add $4$ and $1$ .

$- \frac{5}{2} - 5 \cdot x = - 27 \frac{1}{2}$

$- \frac{5}{2} - 5 x = - 27 \frac{1}{2}$

Step 2

Simplify the right side.

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Step 2.1

Convert $27 \frac{1}{2}$ to an improper fraction.

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Step 2.1.1

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

$- \frac{5}{2} - 5 x = - (27 + \frac{1}{2})$

Step 2.1.2

Add $27$ and $\frac{1}{2}$ .

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Step 2.1.2.1

To write $27$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{5}{2} - 5 x = - (27 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.1.2.2

Combine $27$ and $\frac{2}{2}$ .

$- \frac{5}{2} - 5 x = - (\frac{27 \cdot 2}{2} + \frac{1}{2})$

Step 2.1.2.3

Combine the numerators over the common denominator.

$- \frac{5}{2} - 5 x = - \frac{27 \cdot 2 + 1}{2}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $27$ by $2$ .

$- \frac{5}{2} - 5 x = - \frac{54 + 1}{2}$

Step 2.1.2.4.2

Add $54$ and $1$ .

$- \frac{5}{2} - 5 x = - \frac{55}{2}$

Step 3

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

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Step 3.1

Add $\frac{5}{2}$ to both sides of the equation.

$- 5 x = - \frac{55}{2} + \frac{5}{2}$

Step 3.2

Combine the numerators over the common denominator.

$- 5 x = \frac{- 55 + 5}{2}$

Step 3.3

Add $- 55$ and $5$ .

$- 5 x = \frac{- 50}{2}$

Step 3.4

Divide $- 50$ by $2$ .

$- 5 x = - 25$

Step 4

Divide each term in $- 5 x = - 25$ by $- 5$ and simplify.

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Step 4.1

Divide each term in $- 5 x = - 25$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 25}{- 5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 25}{- 5}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 25}{- 5}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 25$ by $- 5$ .

$x = 5$