Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Combine $m$ and $\frac{3}{4}$ .

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

Step 1.2

Move $3$ to the left of $m$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

Subtract $\frac{m}{4}$ from both sides of the equation.

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Subtract $m$ from $- 3 m$ .

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

Step 3.4

Simplify each term.

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Step 3.4.1

Cancel the common factor of $- 4$ and $4$ .

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Step 3.4.1.1

Factor $4$ out of $- 4 m$ .

$\frac{4 (- m)}{4} + \frac{- 1}{2} = 2$

Step 3.4.1.2

Cancel the common factors.

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Step 3.4.1.2.1

Factor $4$ out of $4$ .

$\frac{4 (- m)}{4 (1)} + \frac{- 1}{2} = 2$

Step 3.4.1.2.2

Cancel the common factor.

$\frac{4 (- m)}{4 \cdot 1} + \frac{- 1}{2} = 2$

Step 3.4.1.2.3

Rewrite the expression.

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

Step 3.4.1.2.4

Divide $- m$ by $1$ .

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

Step 3.4.2

Move the negative in front of the fraction.

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

Step 4

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

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Step 4.1

Add $\frac{1}{2}$ to both sides of the equation.

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $2$ by $2$ .

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

Step 4.5.2

Add $4$ and $1$ .

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

Step 5

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

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Step 5.1

Divide each term in $- m = \frac{5}{2}$ by $- 1$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

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

Step 5.2.2

Divide $m$ by $1$ .

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

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative one from the denominator of $\frac{\frac{5}{2}}{- 1}$ .

$m = - 1 \cdot \frac{5}{2}$

Step 5.3.2

Rewrite $- 1 \cdot \frac{5}{2}$ as $- \frac{5}{2}$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$m = - 2.5$

Mixed Number Form:

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