Algebra Examples

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

Step 1

Simplify the left side.

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Step 1.1

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

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Step 1.1.1

Convert $2 \frac{1}{3}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

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

Step 1.1.1.2

Add $2$ and $\frac{1}{3}$ .

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Step 1.1.1.2.1

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

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

Step 1.1.1.2.2

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

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

Step 1.1.1.2.3

Combine the numerators over the common denominator.

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

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $2$ by $3$ .

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

Step 1.1.1.2.4.2

Add $6$ and $1$ .

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

Step 1.1.2

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

$\frac{7}{3} - \frac{x}{2} = - \frac{2}{3}$

Step 2

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

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Step 2.1

Subtract $\frac{7}{3}$ from both sides of the equation.

$- \frac{x}{2} = - \frac{2}{3} - \frac{7}{3}$

Step 2.2

Combine the numerators over the common denominator.

$- \frac{x}{2} = \frac{- 2 - 7}{3}$

Step 2.3

Subtract $7$ from $- 2$ .

$- \frac{x}{2} = \frac{- 9}{3}$

Step 2.4

Divide $- 9$ by $3$ .

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

Step 3

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

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

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

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

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

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

Step 4.1.1.1.2

Factor $2$ out of $- 2$ .

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

Step 4.1.1.1.3

Cancel the common factor.

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

Step 4.1.1.1.4

Rewrite the expression.

$- - x = - 2 \cdot - 3$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot - 3$

Step 4.1.1.2.2

Multiply $x$ by $1$ .

$x = - 2 \cdot - 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 2$ by $- 3$ .

$x = 6$