Algebra Examples

$5 (- \frac{1}{2} x - \frac{1}{2}) - 2 x = \frac{9}{2} - 6 (x - 1)$

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $x$ and $\frac{1}{2}$ .

$5 (- \frac{x}{2} - \frac{1}{2}) - 2 x = \frac{9}{2} - 6 (x - 1)$

Step 1.1.2

Apply the distributive property.

$5 (- \frac{x}{2}) + 5 (- \frac{1}{2}) - 2 x = \frac{9}{2} - 6 (x - 1)$

Step 1.1.3

Multiply $5 (- \frac{x}{2})$ .

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Step 1.1.3.1

Multiply $- 1$ by $5$ .

$- 5 \frac{x}{2} + 5 (- \frac{1}{2}) - 2 x = \frac{9}{2} - 6 (x - 1)$

Step 1.1.3.2

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

$\frac{- 5 x}{2} + 5 (- \frac{1}{2}) - 2 x = \frac{9}{2} - 6 (x - 1)$

Step 1.1.4

Multiply $5 (- \frac{1}{2})$ .

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Step 1.1.4.1

Multiply $- 1$ by $5$ .

$\frac{- 5 x}{2} - 5 (\frac{1}{2}) - 2 x = \frac{9}{2} - 6 (x - 1)$

Step 1.1.4.2

Combine $- 5$ and $\frac{1}{2}$ .

$\frac{- 5 x}{2} + \frac{- 5}{2} - 2 x = \frac{9}{2} - 6 (x - 1)$

Step 1.1.5

Simplify each term.

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Step 1.1.5.1

Move the negative in front of the fraction.

$- \frac{5 x}{2} + \frac{- 5}{2} - 2 x = \frac{9}{2} - 6 (x - 1)$

Step 1.1.5.2

Move the negative in front of the fraction.

$- \frac{5 x}{2} - \frac{5}{2} - 2 x = \frac{9}{2} - 6 (x - 1)$

Step 1.2

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

$- \frac{5 x}{2} - 2 x \cdot \frac{2}{2} - \frac{5}{2} = \frac{9}{2} - 6 (x - 1)$

Step 1.3

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

$- \frac{5 x}{2} + \frac{- 2 x \cdot 2}{2} - \frac{5}{2} = \frac{9}{2} - 6 (x - 1)$

Step 1.4

Combine the numerators over the common denominator.

$\frac{- 5 x - 2 x \cdot 2}{2} - \frac{5}{2} = \frac{9}{2} - 6 (x - 1)$

Step 1.5

Combine the numerators over the common denominator.

$\frac{- 5 x - 2 x \cdot 2 - 5}{2} = \frac{9}{2} - 6 (x - 1)$

Step 1.6

Multiply $2$ by $- 2$ .

$\frac{- 5 x - 4 x - 5}{2} = \frac{9}{2} - 6 (x - 1)$

Step 1.7

Subtract $4 x$ from $- 5 x$ .

$\frac{- 9 x - 5}{2} = \frac{9}{2} - 6 (x - 1)$

Step 1.8

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

$\frac{- (9 x) - 5}{2} = \frac{9}{2} - 6 (x - 1)$

Step 1.9

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{- (9 x) - 1 (5)}{2} = \frac{9}{2} - 6 (x - 1)$

Step 1.10

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

$\frac{- (9 x + 5)}{2} = \frac{9}{2} - 6 (x - 1)$

Step 1.11

Simplify the expression.

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Step 1.11.1

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

$\frac{- 1 (9 x + 5)}{2} = \frac{9}{2} - 6 (x - 1)$

Step 1.11.2

Move the negative in front of the fraction.

$- \frac{9 x + 5}{2} = \frac{9}{2} - 6 (x - 1)$

Step 2

Simplify $\frac{9}{2} - 6 (x - 1)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- \frac{9 x + 5}{2} = \frac{9}{2} - 6 x - 6 \cdot - 1$

Step 2.1.2

Multiply $- 6$ by $- 1$ .

$- \frac{9 x + 5}{2} = \frac{9}{2} - 6 x + 6$

Step 2.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{9 x + 5}{2} = - 6 x + \frac{9}{2} + 6 \cdot \frac{2}{2}$

Step 2.3

Combine $6$ and $\frac{2}{2}$ .

$- \frac{9 x + 5}{2} = - 6 x + \frac{9}{2} + \frac{6 \cdot 2}{2}$

Step 2.4

Combine the numerators over the common denominator.

$- \frac{9 x + 5}{2} = - 6 x + \frac{9 + 6 \cdot 2}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $6$ by $2$ .

$- \frac{9 x + 5}{2} = - 6 x + \frac{9 + 12}{2}$

Step 2.5.2

Add $9$ and $12$ .

$- \frac{9 x + 5}{2} = - 6 x + \frac{21}{2}$

Step 3

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

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Step 3.1

Add $6 x$ to both sides of the equation.

$- \frac{9 x + 5}{2} + 6 x = \frac{21}{2}$

Step 3.2

To write $6 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{9 x + 5}{2} + 6 x \cdot \frac{2}{2} = \frac{21}{2}$

Step 3.3

Combine $6 x$ and $\frac{2}{2}$ .

$- \frac{9 x + 5}{2} + \frac{6 x \cdot 2}{2} = \frac{21}{2}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{- (9 x + 5) + 6 x \cdot 2}{2} = \frac{21}{2}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Apply the distributive property.

$\frac{- (9 x) - 1 \cdot 5 + 6 x \cdot 2}{2} = \frac{21}{2}$

Step 3.5.2

Multiply $9$ by $- 1$ .

$\frac{- 9 x - 1 \cdot 5 + 6 x \cdot 2}{2} = \frac{21}{2}$

Step 3.5.3

Multiply $- 1$ by $5$ .

$\frac{- 9 x - 5 + 6 x \cdot 2}{2} = \frac{21}{2}$

Step 3.5.4

Multiply $2$ by $6$ .

$\frac{- 9 x - 5 + 12 x}{2} = \frac{21}{2}$

Step 3.5.5

Add $- 9 x$ and $12 x$ .

$\frac{3 x - 5}{2} = \frac{21}{2}$

Step 4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$3 x - 5 = 21$

Step 5

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

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Step 5.1

Add $5$ to both sides of the equation.

$3 x = 21 + 5$

Step 5.2

Add $21$ and $5$ .

$3 x = 26$

Step 6

Divide each term in $3 x = 26$ by $3$ and simplify.

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Step 6.1

Divide each term in $3 x = 26$ by $3$ .

$\frac{3 x}{3} = \frac{26}{3}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $3$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{26}{3}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{26}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{26}{3}$

Decimal Form:

$x = 8.\overline{6}$

Mixed Number Form:

$x = 8 \frac{2}{3}$