Algebra Examples

$- \frac{1}{2} x - \frac{1}{2} (9 x + 4) + \frac{7}{4} = - (- x + 1)$

Step 1

Simplify $- \frac{1}{2} x - \frac{1}{2} \cdot (9 x + 4) + \frac{7}{4}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$- \frac{x}{2} - \frac{1}{2} \cdot (9 x + 4) + \frac{7}{4} = - (- x + 1)$

Step 1.1.2

Apply the distributive property.

$- \frac{x}{2} - \frac{1}{2} (9 x) - \frac{1}{2} \cdot 4 + \frac{7}{4} = - (- x + 1)$

Step 1.1.3

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

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Step 1.1.3.1

Multiply $9$ by $- 1$ .

$- \frac{x}{2} - 9 (\frac{1}{2}) x - \frac{1}{2} \cdot 4 + \frac{7}{4} = - (- x + 1)$

Step 1.1.3.2

Combine $- 9$ and $\frac{1}{2}$ .

$- \frac{x}{2} + \frac{- 9}{2} x - \frac{1}{2} \cdot 4 + \frac{7}{4} = - (- x + 1)$

Step 1.1.3.3

Combine $\frac{- 9}{2}$ and $x$ .

$- \frac{x}{2} + \frac{- 9 x}{2} - \frac{1}{2} \cdot 4 + \frac{7}{4} = - (- x + 1)$

Step 1.1.4

Cancel the common factor of $2$ .

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Step 1.1.4.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- \frac{x}{2} + \frac{- 9 x}{2} + \frac{- 1}{2} \cdot 4 + \frac{7}{4} = - (- x + 1)$

Step 1.1.4.2

Factor $2$ out of $4$ .

$- \frac{x}{2} + \frac{- 9 x}{2} + \frac{- 1}{2} \cdot (2 (2)) + \frac{7}{4} = - (- x + 1)$

Step 1.1.4.3

Cancel the common factor.

$- \frac{x}{2} + \frac{- 9 x}{2} + \frac{- 1}{2} \cdot (2 \cdot 2) + \frac{7}{4} = - (- x + 1)$

Step 1.1.4.4

Rewrite the expression.

$- \frac{x}{2} + \frac{- 9 x}{2} - 1 \cdot 2 + \frac{7}{4} = - (- x + 1)$

Step 1.1.5

Multiply $- 1$ by $2$ .

$- \frac{x}{2} + \frac{- 9 x}{2} - 2 + \frac{7}{4} = - (- x + 1)$

Step 1.1.6

Move the negative in front of the fraction.

$- \frac{x}{2} - \frac{9 x}{2} - 2 + \frac{7}{4} = - (- x + 1)$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$- 2 + \frac{- x - 9 x}{2} + \frac{7}{4} = - (- x + 1)$

Step 1.2.2

Subtract $9 x$ from $- x$ .

$- 2 + \frac{- 10 x}{2} + \frac{7}{4} = - (- x + 1)$

Step 1.2.3

Cancel the common factor of $- 10$ and $2$ .

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Step 1.2.3.1

Factor $2$ out of $- 10 x$ .

$- 2 + \frac{2 (- 5 x)}{2} + \frac{7}{4} = - (- x + 1)$

Step 1.2.3.2

Cancel the common factors.

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Step 1.2.3.2.1

Factor $2$ out of $2$ .

$- 2 + \frac{2 (- 5 x)}{2 (1)} + \frac{7}{4} = - (- x + 1)$

Step 1.2.3.2.2

Cancel the common factor.

$- 2 + \frac{2 (- 5 x)}{2 \cdot 1} + \frac{7}{4} = - (- x + 1)$

Step 1.2.3.2.3

Rewrite the expression.

$- 2 + \frac{- 5 x}{1} + \frac{7}{4} = - (- x + 1)$

Step 1.2.3.2.4

Divide $- 5 x$ by $1$ .

$- 2 - 5 x + \frac{7}{4} = - (- x + 1)$

Step 1.3

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 5 x - 2 \cdot \frac{4}{4} + \frac{7}{4} = - (- x + 1)$

Step 1.4

Combine $- 2$ and $\frac{4}{4}$ .

$- 5 x + \frac{- 2 \cdot 4}{4} + \frac{7}{4} = - (- x + 1)$

Step 1.5

Combine the numerators over the common denominator.

$- 5 x + \frac{- 2 \cdot 4 + 7}{4} = - (- x + 1)$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $- 2$ by $4$ .

$- 5 x + \frac{- 8 + 7}{4} = - (- x + 1)$

Step 1.6.2

Add $- 8$ and $7$ .

$- 5 x + \frac{- 1}{4} = - (- x + 1)$

Step 1.7

Move the negative in front of the fraction.

$- 5 x - \frac{1}{4} = - (- x + 1)$

Step 2

Simplify $- (- x + 1)$ .

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Step 2.1

Apply the distributive property.

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

Step 2.2

Multiply $- - x$ .

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Step 2.2.1

Multiply $- 1$ by $- 1$ .

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

Step 2.2.2

Multiply $x$ by $1$ .

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

Step 2.3

Multiply $- 1$ by $1$ .

$- 5 x - \frac{1}{4} = x - 1$

Step 3

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

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Step 3.1

Subtract $x$ from both sides of the equation.

$- 5 x - \frac{1}{4} - x = - 1$

Step 3.2

Subtract $x$ from $- 5 x$ .

$- 6 x - \frac{1}{4} = - 1$

Step 4

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

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Step 4.1

Add $\frac{1}{4}$ to both sides of the equation.

$- 6 x = - 1 + \frac{1}{4}$

Step 4.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- 6 x = - 1 \cdot \frac{4}{4} + \frac{1}{4}$

Step 4.3

Combine $- 1$ and $\frac{4}{4}$ .

$- 6 x = \frac{- 1 \cdot 4}{4} + \frac{1}{4}$

Step 4.4

Combine the numerators over the common denominator.

$- 6 x = \frac{- 1 \cdot 4 + 1}{4}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 1$ by $4$ .

$- 6 x = \frac{- 4 + 1}{4}$

Step 4.5.2

Add $- 4$ and $1$ .

$- 6 x = \frac{- 3}{4}$

Step 4.6

Move the negative in front of the fraction.

$- 6 x = - \frac{3}{4}$

Step 5

Divide each term in $- 6 x = - \frac{3}{4}$ by $- 6$ and simplify.

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Step 5.1

Divide each term in $- 6 x = - \frac{3}{4}$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- \frac{3}{4}}{- 6}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 6$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- \frac{3}{4}}{- 6}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{3}{4}}{- 6}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{3}{4} \cdot \frac{1}{- 6}$

Step 5.3.2

Cancel the common factor of $3$ .

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Step 5.3.2.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$x = \frac{- 3}{4} \cdot \frac{1}{- 6}$

Step 5.3.2.2

Factor $3$ out of $- 3$ .

$x = \frac{3 (- 1)}{4} \cdot \frac{1}{- 6}$

Step 5.3.2.3

Factor $3$ out of $- 6$ .

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

Step 5.3.2.4

Cancel the common factor.

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

Step 5.3.2.5

Rewrite the expression.

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

Step 5.3.3

Multiply $\frac{- 1}{4}$ by $\frac{1}{- 2}$ .

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

Step 5.3.4

Multiply $4$ by $- 2$ .

$x = \frac{- 1}{- 8}$

Step 5.3.5

Dividing two negative values results in a positive value.

$x = \frac{1}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{8}$

Decimal Form:

$x = 0.125$