Algebra Examples

$(1 - \frac{2}{3} m_{2}) (1) = m_{2} + \frac{2}{3}$

Step 1

Simplify $(1 - \frac{2}{3} m_{2}) \cdot 1$ .

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Step 1.1

Rewrite.

$0 + 0 + (1 - \frac{2}{3} m_{2}) \cdot 1 = m_{2} + \frac{2}{3}$

Step 1.2

Simplify by adding zeros.

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

Step 1.3

Simplify each term.

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Step 1.3.1

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

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

Step 1.3.2

Move $2$ to the left of $m_{2}$ .

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

Step 1.4

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

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

Step 2

Move all terms containing $m_{2}$ to the left side of the equation.

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Step 2.1

Subtract $m_{2}$ from both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $m_{2}$ out of $- 2 m_{2} - m_{2} \cdot 3$ .

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Step 2.5.1.1.1

Factor $m_{2}$ out of $- 2 m_{2}$ .

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

Step 2.5.1.1.2

Factor $m_{2}$ out of $- m_{2} \cdot 3$ .

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

Step 2.5.1.1.3

Factor $m_{2}$ out of $m_{2} \cdot - 2 + m_{2} (- 1 \cdot 3)$ .

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

Step 2.5.1.2

Multiply $- 1$ by $3$ .

$1 + \frac{m_{2} (- 2 - 3)}{3} = \frac{2}{3}$

Step 2.5.1.3

Subtract $3$ from $- 2$ .

$1 + \frac{m_{2} \cdot - 5}{3} = \frac{2}{3}$

Step 2.5.2

Move $- 5$ to the left of $m_{2}$ .

$1 + \frac{- 5 \cdot m_{2}}{3} = \frac{2}{3}$

Step 2.5.3

Move the negative in front of the fraction.

$1 - \frac{5 m_{2}}{3} = \frac{2}{3}$

Step 3

Move all terms not containing $m_{2}$ to the right side of the equation.

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Step 3.1

Subtract $1$ from both sides of the equation.

$- \frac{5 m_{2}}{3} = \frac{2}{3} - 1$

Step 3.2

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

$- \frac{5 m_{2}}{3} = \frac{2}{3} - 1 \cdot \frac{3}{3}$

Step 3.3

Combine $- 1$ and $\frac{3}{3}$ .

$- \frac{5 m_{2}}{3} = \frac{2}{3} + \frac{- 1 \cdot 3}{3}$

Step 3.4

Combine the numerators over the common denominator.

$- \frac{5 m_{2}}{3} = \frac{2 - 1 \cdot 3}{3}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 1$ by $3$ .

$- \frac{5 m_{2}}{3} = \frac{2 - 3}{3}$

Step 3.5.2

Subtract $3$ from $2$ .

$- \frac{5 m_{2}}{3} = \frac{- 1}{3}$

Step 3.6

Move the negative in front of the fraction.

$- \frac{5 m_{2}}{3} = - \frac{1}{3}$

Step 4

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

$- 5 m_{2} = - 1$

Step 5

Divide each term in $- 5 m_{2} = - 1$ by $- 5$ and simplify.

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Step 5.1

Divide each term in $- 5 m_{2} = - 1$ by $- 5$ .

$\frac{- 5 m_{2}}{- 5} = \frac{- 1}{- 5}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 5 m_{2}}{- 5} = \frac{- 1}{- 5}$

Step 5.2.1.2

Divide $m_{2}$ by $1$ .

$m_{2} = \frac{- 1}{- 5}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Dividing two negative values results in a positive value.

$m_{2} = \frac{1}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m_{2} = \frac{1}{5}$

Decimal Form:

$m_{2} = 0.2$