Algebra Examples

$\frac{5}{4} m - 2 = - m + \frac{1}{2} - \frac{7}{4} + \frac{1}{2} m$

Step 1

Since $m$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- m + \frac{1}{2} - \frac{7}{4} + \frac{1}{2} m = \frac{5}{4} m - 2$

Step 2

Simplify $- m + \frac{1}{2} - \frac{7}{4} + \frac{1}{2} m$ .

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Step 2.1

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

$- m + \frac{1}{2} - \frac{7}{4} + \frac{m}{2} = \frac{5}{4} m - 2$

Step 2.2

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

$- m \cdot \frac{2}{2} + \frac{m}{2} + \frac{1}{2} - \frac{7}{4} = \frac{5}{4} m - 2$

Step 2.3

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

$\frac{- m \cdot 2}{2} + \frac{m}{2} + \frac{1}{2} - \frac{7}{4} = \frac{5}{4} m - 2$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- m \cdot 2 + m}{2} + \frac{1}{2} - \frac{7}{4} = \frac{5}{4} m - 2$

Step 2.5

Combine the numerators over the common denominator.

$\frac{- m \cdot 2 + m + 1}{2} + \frac{- 7}{4} = \frac{5}{4} m - 2$

Step 2.6

Multiply $2$ by $- 1$ .

$\frac{- 2 m + m + 1}{2} + \frac{- 7}{4} = \frac{5}{4} m - 2$

Step 2.7

Add $- 2 m$ and $m$ .

$\frac{- m + 1}{2} + \frac{- 7}{4} = \frac{5}{4} m - 2$

Step 2.8

Move the negative in front of the fraction.

$\frac{- m + 1}{2} - \frac{7}{4} = \frac{5}{4} m - 2$

Step 2.9

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

$\frac{- m + 1}{2} \cdot \frac{2}{2} - \frac{7}{4} = \frac{5}{4} m - 2$

Step 2.10

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.10.1

Multiply $\frac{- m + 1}{2}$ by $\frac{2}{2}$ .

$\frac{(- m + 1) \cdot 2}{2 \cdot 2} - \frac{7}{4} = \frac{5}{4} m - 2$

Step 2.10.2

Multiply $2$ by $2$ .

$\frac{(- m + 1) \cdot 2}{4} - \frac{7}{4} = \frac{5}{4} m - 2$

Step 2.11

Combine the numerators over the common denominator.

$\frac{(- m + 1) \cdot 2 - 7}{4} = \frac{5}{4} m - 2$

Step 2.12

Simplify the numerator.

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Step 2.12.1

Apply the distributive property.

$\frac{- m \cdot 2 + 1 \cdot 2 - 7}{4} = \frac{5}{4} m - 2$

Step 2.12.2

Multiply $2$ by $- 1$ .

$\frac{- 2 m + 1 \cdot 2 - 7}{4} = \frac{5}{4} m - 2$

Step 2.12.3

Multiply $2$ by $1$ .

$\frac{- 2 m + 2 - 7}{4} = \frac{5}{4} m - 2$

Step 2.12.4

Subtract $7$ from $2$ .

$\frac{- 2 m - 5}{4} = \frac{5}{4} m - 2$

Step 2.13

Simplify with factoring out.

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Step 2.13.1

Factor $- 1$ out of $- 2 m$ .

$\frac{- (2 m) - 5}{4} = \frac{5}{4} m - 2$

Step 2.13.2

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{- (2 m) - 1 (5)}{4} = \frac{5}{4} m - 2$

Step 2.13.3

Factor $- 1$ out of $- (2 m) - 1 (5)$ .

$\frac{- (2 m + 5)}{4} = \frac{5}{4} m - 2$

Step 2.13.4

Simplify the expression.

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Step 2.13.4.1

Rewrite $- (2 m + 5)$ as $- 1 (2 m + 5)$ .

$\frac{- 1 (2 m + 5)}{4} = \frac{5}{4} m - 2$

Step 2.13.4.2

Move the negative in front of the fraction.

$- \frac{2 m + 5}{4} = \frac{5}{4} m - 2$

Step 3

Combine $\frac{5}{4}$ and $m$ .

$- \frac{2 m + 5}{4} = \frac{5 m}{4} - 2$

Step 4

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

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Step 4.1

Subtract $\frac{5 m}{4}$ from both sides of the equation.

$- \frac{2 m + 5}{4} - \frac{5 m}{4} = - 2$

Step 4.2

Combine the numerators over the common denominator.

$\frac{- (2 m + 5) - 5 m}{4} = - 2$

Step 4.3

Simplify each term.

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Step 4.3.1

Apply the distributive property.

$\frac{- (2 m) - 1 \cdot 5 - 5 m}{4} = - 2$

Step 4.3.2

Multiply $2$ by $- 1$ .

$\frac{- 2 m - 1 \cdot 5 - 5 m}{4} = - 2$

Step 4.3.3

Multiply $- 1$ by $5$ .

$\frac{- 2 m - 5 - 5 m}{4} = - 2$

Step 4.4

Subtract $5 m$ from $- 2 m$ .

$\frac{- 7 m - 5}{4} = - 2$

Step 4.5

Factor $- 1$ out of $- 7 m$ .

$\frac{- (7 m) - 5}{4} = - 2$

Step 4.6

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{- (7 m) - 1 (5)}{4} = - 2$

Step 4.7

Factor $- 1$ out of $- (7 m) - 1 (5)$ .

$\frac{- (7 m + 5)}{4} = - 2$

Step 4.8

Rewrite $- (7 m + 5)$ as $- 1 (7 m + 5)$ .

$\frac{- 1 (7 m + 5)}{4} = - 2$

Step 4.9

Move the negative in front of the fraction.

$- \frac{7 m + 5}{4} = - 2$

Step 5

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{7 m + 5}{4}) = - 4 \cdot - 2$

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 $- 4 (- \frac{7 m + 5}{4})$ .

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Step 6.1.1.1

Cancel the common factor of $4$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{7 m + 5}{4}$ into the numerator.

$- 4 \frac{- (7 m + 5)}{4} = - 4 \cdot - 2$

Step 6.1.1.1.2

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- (7 m + 5)}{4} = - 4 \cdot - 2$

Step 6.1.1.1.3

Cancel the common factor.

$4 \cdot - 1 \frac{- (7 m + 5)}{4} = - 4 \cdot - 2$

Step 6.1.1.1.4

Rewrite the expression.

$- - (7 m + 5) = - 4 \cdot - 2$

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (7 m + 5) = - 4 \cdot - 2$

Step 6.1.1.2.2

Multiply $7 m + 5$ by $1$ .

$7 m + 5 = - 4 \cdot - 2$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- 4$ by $- 2$ .

$7 m + 5 = 8$

Step 7

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

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Step 7.1

Subtract $5$ from both sides of the equation.

$7 m = 8 - 5$

Step 7.2

Subtract $5$ from $8$ .

$7 m = 3$

Step 8

Divide each term in $7 m = 3$ by $7$ and simplify.

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Step 8.1

Divide each term in $7 m = 3$ by $7$ .

$\frac{7 m}{7} = \frac{3}{7}$

Step 8.2

Simplify the left side.

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Step 8.2.1

Cancel the common factor of $7$ .

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Step 8.2.1.1

Cancel the common factor.

$\frac{7 m}{7} = \frac{3}{7}$

Step 8.2.1.2

Divide $m$ by $1$ .

$m = \frac{3}{7}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$m = \frac{3}{7}$

Decimal Form:

$m = 0.\overline{428571}$