Algebra Examples

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

Step 1

Simplify $\frac{2}{3} m - 2 + \frac{1}{6} m + \frac{3}{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

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

Step 1.1.2

Combine $\frac{1}{6}$ and $m$ .

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $3$ by $2$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Find the common denominator.

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Step 1.5.1

Write $- 2$ as a fraction with denominator $1$ .

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

Step 1.5.2

Multiply $\frac{- 2}{1}$ by $\frac{6}{6}$ .

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

Step 1.5.3

Multiply $\frac{- 2}{1}$ by $\frac{6}{6}$ .

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

Step 1.5.4

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

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

Step 1.5.5

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

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

Step 1.5.6

Multiply $2$ by $3$ .

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

Step 1.6

Combine the numerators over the common denominator.

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

Step 1.7

Simplify each term.

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Step 1.7.1

Multiply $2$ by $2$ .

$\frac{4 m + m - 2 \cdot 6 + 3 \cdot 3}{6} = \frac{1}{2} m$

Step 1.7.2

Multiply $- 2$ by $6$ .

$\frac{4 m + m - 12 + 3 \cdot 3}{6} = \frac{1}{2} m$

Step 1.7.3

Multiply $3$ by $3$ .

$\frac{4 m + m - 12 + 9}{6} = \frac{1}{2} m$

Step 1.8

Simplify by adding terms.

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Step 1.8.1

Add $4 m$ and $m$ .

$\frac{5 m - 12 + 9}{6} = \frac{1}{2} m$

Step 1.8.2

Add $- 12$ and $9$ .

$\frac{5 m - 3}{6} = \frac{1}{2} m$

Step 2

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

$\frac{5 m - 3}{6} = \frac{m}{2}$

Step 3

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

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Step 3.1

Subtract $\frac{m}{2}$ from both sides of the equation.

$\frac{5 m - 3}{6} - \frac{m}{2} = 0$

Step 3.2

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

$\frac{5 m - 3}{6} - \frac{m}{2} \cdot \frac{3}{3} = 0$

Step 3.3

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

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Step 3.3.1

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

$\frac{5 m - 3}{6} - \frac{m \cdot 3}{2 \cdot 3} = 0$

Step 3.3.2

Multiply $2$ by $3$ .

$\frac{5 m - 3}{6} - \frac{m \cdot 3}{6} = 0$

Step 3.4

Combine the numerators over the common denominator.

$\frac{5 m - 3 - m \cdot 3}{6} = 0$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $3$ by $- 1$ .

$\frac{5 m - 3 - 3 m}{6} = 0$

Step 3.5.2

Subtract $3 m$ from $5 m$ .

$\frac{2 m - 3}{6} = 0$

Step 4

Set the numerator equal to zero.

$2 m - 3 = 0$

Step 5

Solve the equation for $m$ .

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Step 5.1

Add $3$ to both sides of the equation.

$2 m = 3$

Step 5.2

Divide each term in $2 m = 3$ by $2$ and simplify.

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Step 5.2.1

Divide each term in $2 m = 3$ by $2$ .

$\frac{2 m}{2} = \frac{3}{2}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $2$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{2 m}{2} = \frac{3}{2}$

Step 5.2.2.1.2

Divide $m$ by $1$ .

$m = \frac{3}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$m = \frac{3}{2}$

Decimal Form:

$m = 1.5$

Mixed Number Form:

$m = 1 \frac{1}{2}$