Algebra Examples

$- (x + \frac{2}{3}) + \frac{1}{2} = \frac{7}{6} - \frac{1}{2} x$

Step 1

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

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Step 1.1

Apply the distributive property.

$- x - \frac{2}{3} + \frac{1}{2} = \frac{7}{6} - \frac{1}{2} x$

Step 1.2

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- x - \frac{2}{3} \cdot \frac{2}{2} + \frac{1}{2} = \frac{7}{6} - \frac{1}{2} x$

Step 1.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- x - \frac{2}{3} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{3}{3} = \frac{7}{6} - \frac{1}{2} x$

Step 1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

$- x - \frac{2 \cdot 2}{3 \cdot 2} + \frac{1}{2} \cdot \frac{3}{3} = \frac{7}{6} - \frac{1}{2} x$

Step 1.4.2

Multiply $3$ by $2$ .

$- x - \frac{2 \cdot 2}{6} + \frac{1}{2} \cdot \frac{3}{3} = \frac{7}{6} - \frac{1}{2} x$

Step 1.4.3

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$- x - \frac{2 \cdot 2}{6} + \frac{3}{2 \cdot 3} = \frac{7}{6} - \frac{1}{2} x$

Step 1.4.4

Multiply $2$ by $3$ .

$- x - \frac{2 \cdot 2}{6} + \frac{3}{6} = \frac{7}{6} - \frac{1}{2} x$

Step 1.5

Combine the numerators over the common denominator.

$- x + \frac{- 2 \cdot 2 + 3}{6} = \frac{7}{6} - \frac{1}{2} x$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $- 2$ by $2$ .

$- x + \frac{- 4 + 3}{6} = \frac{7}{6} - \frac{1}{2} x$

Step 1.6.2

Add $- 4$ and $3$ .

$- x + \frac{- 1}{6} = \frac{7}{6} - \frac{1}{2} x$

Step 1.7

Move the negative in front of the fraction.

$- x - \frac{1}{6} = \frac{7}{6} - \frac{1}{2} x$

Step 2

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

$- x - \frac{1}{6} = \frac{7}{6} - \frac{x}{2}$

Step 3

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

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Step 3.1

Add $\frac{x}{2}$ to both sides of the equation.

$- x - \frac{1}{6} + \frac{x}{2} = \frac{7}{6}$

Step 3.2

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

$- x \cdot \frac{2}{2} + \frac{x}{2} - \frac{1}{6} = \frac{7}{6}$

Step 3.3

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

$\frac{- x \cdot 2}{2} + \frac{x}{2} - \frac{1}{6} = \frac{7}{6}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{- x \cdot 2 + x}{2} - \frac{1}{6} = \frac{7}{6}$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $x$ out of $- x \cdot 2 + x$ .

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Step 3.5.1.1.1

Factor $x$ out of $- x \cdot 2$ .

$\frac{x (- 1 \cdot 2) + x}{2} - \frac{1}{6} = \frac{7}{6}$

Step 3.5.1.1.2

Raise $x$ to the power of $1$ .

$\frac{x (- 1 \cdot 2) + x^{1}}{2} - \frac{1}{6} = \frac{7}{6}$

Step 3.5.1.1.3

Factor $x$ out of $x^{1}$ .

$\frac{x (- 1 \cdot 2) + x \cdot 1}{2} - \frac{1}{6} = \frac{7}{6}$

Step 3.5.1.1.4

Factor $x$ out of $x (- 1 \cdot 2) + x \cdot 1$ .

$\frac{x (- 1 \cdot 2 + 1)}{2} - \frac{1}{6} = \frac{7}{6}$

Step 3.5.1.2

Multiply $- 1$ by $2$ .

$\frac{x (- 2 + 1)}{2} - \frac{1}{6} = \frac{7}{6}$

Step 3.5.1.3

Add $- 2$ and $1$ .

$\frac{x \cdot - 1}{2} - \frac{1}{6} = \frac{7}{6}$

Step 3.5.2

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{2} - \frac{1}{6} = \frac{7}{6}$

Step 3.5.3

Move the negative in front of the fraction.

$- \frac{x}{2} - \frac{1}{6} = \frac{7}{6}$

Step 4

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

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Step 4.1

Add $\frac{1}{6}$ to both sides of the equation.

$- \frac{x}{2} = \frac{7}{6} + \frac{1}{6}$

Step 4.2

Combine the numerators over the common denominator.

$- \frac{x}{2} = \frac{7 + 1}{6}$

Step 4.3

Add $7$ and $1$ .

$- \frac{x}{2} = \frac{8}{6}$

Step 4.4

Cancel the common factor of $8$ and $6$ .

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Step 4.4.1

Factor $2$ out of $8$ .

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

Step 4.4.2

Cancel the common factors.

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Step 4.4.2.1

Factor $2$ out of $6$ .

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

Step 4.4.2.2

Cancel the common factor.

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

Step 4.4.2.3

Rewrite the expression.

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

Step 5

Multiply both sides of the equation by $- 2$ .

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

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

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

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Step 6.1.1.1

Cancel the common factor of $2$ .

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Step 6.1.1.1.1

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

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

Step 6.1.1.1.2

Factor $2$ out of $- 2$ .

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

Step 6.1.1.1.3

Cancel the common factor.

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

Step 6.1.1.1.4

Rewrite the expression.

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

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

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

Step 6.1.1.2.2

Multiply $x$ by $1$ .

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

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- 2 (\frac{4}{3})$ .

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Step 6.2.1.1

Multiply $- 2 (\frac{4}{3})$ .

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Step 6.2.1.1.1

Combine $- 2$ and $\frac{4}{3}$ .

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

Step 6.2.1.1.2

Multiply $- 2$ by $4$ .

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

Step 6.2.1.2

Move the negative in front of the fraction.

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 2.\overline{6}$

Mixed Number Form:

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