Algebra Examples

$- 2 x = - x - (\frac{3}{2} x - \frac{1}{2}) - 5$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- x - (\frac{3}{2} x - \frac{1}{2}) - 5 = - 2 x$

Step 2

Simplify $- x - (\frac{3}{2} x - \frac{1}{2}) - 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $\frac{3}{2}$ and $x$ .

$- x - (\frac{3 x}{2} - \frac{1}{2}) - 5 = - 2 x$

Step 2.1.2

Apply the distributive property.

$- x - \frac{3 x}{2} - - \frac{1}{2} - 5 = - 2 x$

Step 2.1.3

Multiply $- - \frac{1}{2}$ .

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Step 2.1.3.1

Multiply $- 1$ by $- 1$ .

$- x - \frac{3 x}{2} + 1 (\frac{1}{2}) - 5 = - 2 x$

Step 2.1.3.2

Multiply $\frac{1}{2}$ by $1$ .

$- x - \frac{3 x}{2} + \frac{1}{2} - 5 = - 2 x$

Step 2.2

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

$- x \cdot \frac{2}{2} - \frac{3 x}{2} + \frac{1}{2} - 5 = - 2 x$

Step 2.3

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

$\frac{- x \cdot 2}{2} - \frac{3 x}{2} + \frac{1}{2} - 5 = - 2 x$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- x \cdot 2 - 3 x}{2} + \frac{1}{2} - 5 = - 2 x$

Step 2.5

Combine the numerators over the common denominator.

$- 5 + \frac{- x \cdot 2 - 3 x + 1}{2} = - 2 x$

Step 2.6

Multiply $2$ by $- 1$ .

$- 5 + \frac{- 2 x - 3 x + 1}{2} = - 2 x$

Step 2.7

Subtract $3 x$ from $- 2 x$ .

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

Step 2.8

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

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

Step 2.9

Simplify terms.

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Step 2.9.1

Combine $- 5$ and $\frac{2}{2}$ .

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

Step 2.9.2

Combine the numerators over the common denominator.

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

Step 2.10

Simplify the numerator.

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Step 2.10.1

Multiply $- 5$ by $2$ .

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

Step 2.10.2

Add $- 10$ and $1$ .

$\frac{- 5 x - 9}{2} = - 2 x$

Step 2.11

Simplify with factoring out.

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Step 2.11.1

Factor $- 1$ out of $- 5 x$ .

$\frac{- (5 x) - 9}{2} = - 2 x$

Step 2.11.2

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{- (5 x) - 1 (9)}{2} = - 2 x$

Step 2.11.3

Factor $- 1$ out of $- (5 x) - 1 (9)$ .

$\frac{- (5 x + 9)}{2} = - 2 x$

Step 2.11.4

Simplify the expression.

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Step 2.11.4.1

Rewrite $- (5 x + 9)$ as $- 1 (5 x + 9)$ .

$\frac{- 1 (5 x + 9)}{2} = - 2 x$

Step 2.11.4.2

Move the negative in front of the fraction.

$- \frac{5 x + 9}{2} = - 2 x$

Step 3

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

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Step 3.1

Add $2 x$ to both sides of the equation.

$- \frac{5 x + 9}{2} + 2 x = 0$

Step 3.2

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

$- \frac{5 x + 9}{2} + 2 x \cdot \frac{2}{2} = 0$

Step 3.3

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

$- \frac{5 x + 9}{2} + \frac{2 x \cdot 2}{2} = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{- (5 x + 9) + 2 x \cdot 2}{2} = 0$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Apply the distributive property.

$\frac{- (5 x) - 1 \cdot 9 + 2 x \cdot 2}{2} = 0$

Step 3.5.2

Multiply $5$ by $- 1$ .

$\frac{- 5 x - 1 \cdot 9 + 2 x \cdot 2}{2} = 0$

Step 3.5.3

Multiply $- 1$ by $9$ .

$\frac{- 5 x - 9 + 2 x \cdot 2}{2} = 0$

Step 3.5.4

Multiply $2$ by $2$ .

$\frac{- 5 x - 9 + 4 x}{2} = 0$

Step 3.5.5

Add $- 5 x$ and $4 x$ .

$\frac{- x - 9}{2} = 0$

Step 3.6

Factor $- 1$ out of $- x$ .

$\frac{- (x) - 9}{2} = 0$

Step 3.7

Rewrite $- 9$ as $- 1 (9)$ .

$\frac{- (x) - 1 (9)}{2} = 0$

Step 3.8

Factor $- 1$ out of $- (x) - 1 (9)$ .

$\frac{- (x + 9)}{2} = 0$

Step 3.9

Rewrite $- (x + 9)$ as $- 1 (x + 9)$ .

$\frac{- 1 (x + 9)}{2} = 0$

Step 3.10

Move the negative in front of the fraction.

$- \frac{x + 9}{2} = 0$

Step 4

Set the numerator equal to zero.

$x + 9 = 0$

Step 5

Subtract $9$ from both sides of the equation.

$x = - 9$