Algebra Examples

$- x - (x - 9) - \frac{1}{2} = \frac{3}{2}$

Step 1

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

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Step 1.1

Find the common denominator.

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Step 1.1.1

Write $- x$ as a fraction with denominator $1$ .

$\frac{- x}{1} - (x - 9) - \frac{1}{2} = \frac{3}{2}$

Step 1.1.2

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

$\frac{- x}{1} \cdot \frac{2}{2} - (x - 9) - \frac{1}{2} = \frac{3}{2}$

Step 1.1.3

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

$\frac{- x \cdot 2}{2} - (x - 9) - \frac{1}{2} = \frac{3}{2}$

Step 1.1.4

Write $- (x - 9)$ as a fraction with denominator $1$ .

$\frac{- x \cdot 2}{2} + \frac{- (x - 9)}{1} - \frac{1}{2} = \frac{3}{2}$

Step 1.1.5

Multiply $\frac{- (x - 9)}{1}$ by $\frac{2}{2}$ .

$\frac{- x \cdot 2}{2} + \frac{- (x - 9)}{1} \cdot \frac{2}{2} - \frac{1}{2} = \frac{3}{2}$

Step 1.1.6

Multiply $\frac{- (x - 9)}{1}$ by $\frac{2}{2}$ .

$\frac{- x \cdot 2}{2} + \frac{- (x - 9) \cdot 2}{2} - \frac{1}{2} = \frac{3}{2}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{- x \cdot 2 - (x - 9) \cdot 2 - 1}{2} = \frac{3}{2}$

Step 1.3

Simplify each term.

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Step 1.3.1

Multiply $2$ by $- 1$ .

$\frac{- 2 x - (x - 9) \cdot 2 - 1}{2} = \frac{3}{2}$

Step 1.3.2

Apply the distributive property.

$\frac{- 2 x + (- x - - 9) \cdot 2 - 1}{2} = \frac{3}{2}$

Step 1.3.3

Multiply $- 1$ by $- 9$ .

$\frac{- 2 x + (- x + 9) \cdot 2 - 1}{2} = \frac{3}{2}$

Step 1.3.4

Apply the distributive property.

$\frac{- 2 x - x \cdot 2 + 9 \cdot 2 - 1}{2} = \frac{3}{2}$

Step 1.3.5

Multiply $2$ by $- 1$ .

$\frac{- 2 x - 2 x + 9 \cdot 2 - 1}{2} = \frac{3}{2}$

Step 1.3.6

Multiply $9$ by $2$ .

$\frac{- 2 x - 2 x + 18 - 1}{2} = \frac{3}{2}$

Step 1.4

Simplify terms.

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Step 1.4.1

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

$\frac{- 4 x + 18 - 1}{2} = \frac{3}{2}$

Step 1.4.2

Subtract $1$ from $18$ .

$\frac{- 4 x + 17}{2} = \frac{3}{2}$

Step 1.4.3

Factor $- 1$ out of $- 4 x$ .

$\frac{- (4 x) + 17}{2} = \frac{3}{2}$

Step 1.4.4

Rewrite $17$ as $- 1 (- 17)$ .

$\frac{- (4 x) - 1 (- 17)}{2} = \frac{3}{2}$

Step 1.4.5

Factor $- 1$ out of $- (4 x) - 1 (- 17)$ .

$\frac{- (4 x - 17)}{2} = \frac{3}{2}$

Step 1.4.6

Simplify the expression.

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Step 1.4.6.1

Rewrite $- (4 x - 17)$ as $- 1 (4 x - 17)$ .

$\frac{- 1 (4 x - 17)}{2} = \frac{3}{2}$

Step 1.4.6.2

Move the negative in front of the fraction.

$- \frac{4 x - 17}{2} = \frac{3}{2}$

Step 2

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

$- (4 x - 17) = 3$

Step 3

Simplify $- (4 x - 17)$ .

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Step 3.1

Apply the distributive property.

$- (4 x) - - 17 = 3$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $4$ by $- 1$ .

$- 4 x - - 17 = 3$

Step 3.2.2

Multiply $- 1$ by $- 17$ .

$- 4 x + 17 = 3$

Step 4

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

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Step 4.1

Subtract $17$ from both sides of the equation.

$- 4 x = 3 - 17$

Step 4.2

Subtract $17$ from $3$ .

$- 4 x = - 14$

Step 5

Divide each term in $- 4 x = - 14$ by $- 4$ and simplify.

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Step 5.1

Divide each term in $- 4 x = - 14$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 14}{- 4}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 14}{- 4}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 14}{- 4}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $- 14$ and $- 4$ .

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Step 5.3.1.1

Factor $- 2$ out of $- 14$ .

$x = \frac{- 2 (7)}{- 4}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $- 2$ out of $- 4$ .

$x = \frac{- 2 \cdot 7}{- 2 \cdot 2}$

Step 5.3.1.2.2

Cancel the common factor.

$x = \frac{- 2 \cdot 7}{- 2 \cdot 2}$

Step 5.3.1.2.3

Rewrite the expression.

$x = \frac{7}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{2}$

Decimal Form:

$x = 3.5$

Mixed Number Form:

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