Algebra Examples

$x + 2 - \frac{2 x + 5}{2} = \frac{2 x - 1}{10}$

Step 1

Multiply both sides by $10$ .

$(x + 2 - \frac{2 x + 5}{2}) \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(x + 2 - \frac{2 x + 5}{2}) \cdot 10$ .

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Step 2.1.1.1

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

$(x \cdot \frac{2}{2} - \frac{2 x + 5}{2} + 2) \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.2

Simplify terms.

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Step 2.1.1.2.1

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

$(\frac{x \cdot 2}{2} - \frac{2 x + 5}{2} + 2) \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.2.2

Combine the numerators over the common denominator.

$(\frac{x \cdot 2 - (2 x + 5)}{2} + 2) \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.3

Simplify each term.

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Step 2.1.1.3.1

Simplify the numerator.

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Step 2.1.1.3.1.1

Move $2$ to the left of $x$ .

$(\frac{2 \cdot x - (2 x + 5)}{2} + 2) \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.3.1.2

Apply the distributive property.

$(\frac{2 x - (2 x) - 1 \cdot 5}{2} + 2) \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.3.1.3

Multiply $2$ by $- 1$ .

$(\frac{2 x - 2 x - 1 \cdot 5}{2} + 2) \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.3.1.4

Multiply $- 1$ by $5$ .

$(\frac{2 x - 2 x - 5}{2} + 2) \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.3.1.5

Subtract $2 x$ from $2 x$ .

$(\frac{0 - 5}{2} + 2) \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.3.1.6

Subtract $5$ from $0$ .

$(\frac{- 5}{2} + 2) \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.3.2

Move the negative in front of the fraction.

$(- \frac{5}{2} + 2) \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.4

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

$(- \frac{5}{2} + 2 \cdot \frac{2}{2}) \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.5

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

$(- \frac{5}{2} + \frac{2 \cdot 2}{2}) \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.6

Combine the numerators over the common denominator.

$\frac{- 5 + 2 \cdot 2}{2} \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.7

Simplify the numerator.

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Step 2.1.1.7.1

Multiply $2$ by $2$ .

$\frac{- 5 + 4}{2} \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.7.2

Add $- 5$ and $4$ .

$\frac{- 1}{2} \cdot 10 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.8

Cancel the common factor of $2$ .

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Step 2.1.1.8.1

Factor $2$ out of $10$ .

$\frac{- 1}{2} \cdot (2 (5)) = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.8.2

Cancel the common factor.

$\frac{- 1}{2} \cdot (2 \cdot 5) = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.8.3

Rewrite the expression.

$- 1 \cdot 5 = \frac{2 x - 1}{10} \cdot 10$

Step 2.1.1.9

Multiply $- 1$ by $5$ .

$- 5 = \frac{2 x - 1}{10} \cdot 10$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $10$ .

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Step 2.2.1.1

Cancel the common factor.

$- 5 = \frac{2 x - 1}{10} \cdot 10$

Step 2.2.1.2

Rewrite the expression.

$- 5 = 2 x - 1$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $2 x - 1 = - 5$ .

$2 x - 1 = - 5$

Step 3.2

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

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Step 3.2.1

Add $1$ to both sides of the equation.

$2 x = - 5 + 1$

Step 3.2.2

Add $- 5$ and $1$ .

$2 x = - 4$

Step 3.3

Divide each term in $2 x = - 4$ by $2$ and simplify.

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Step 3.3.1

Divide each term in $2 x = - 4$ by $2$ .

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

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $2$ .

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Step 3.3.2.1.1

Cancel the common factor.

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

Step 3.3.2.1.2

Divide $x$ by $1$ .

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

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 4$ by $2$ .

$x = - 2$