Algebra Examples

$\frac{3}{5} q = \frac{2}{5} q - \frac{1}{2} (\frac{2}{5} q - 6)$

Step 1

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

$\frac{2}{5} q - \frac{1}{2} \cdot (\frac{2}{5} q - 6) = \frac{3}{5} q$

Step 2

Simplify $\frac{2}{5} q - \frac{1}{2} \cdot (\frac{2}{5} q - 6)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $\frac{2}{5}$ and $q$ .

$\frac{2 q}{5} - \frac{1}{2} \cdot (\frac{2}{5} q - 6) = \frac{3}{5} q$

Step 2.1.2

Combine $\frac{2}{5}$ and $q$ .

$\frac{2 q}{5} - \frac{1}{2} \cdot (\frac{2 q}{5} - 6) = \frac{3}{5} q$

Step 2.1.3

Apply the distributive property.

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

Step 2.1.4

Cancel the common factor of $2$ .

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Step 2.1.4.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{2 q}{5} + \frac{- 1}{2} \cdot \frac{2 q}{5} - \frac{1}{2} \cdot - 6 = \frac{3}{5} q$

Step 2.1.4.2

Factor $2$ out of $2 q$ .

$\frac{2 q}{5} + \frac{- 1}{2} \cdot \frac{2 (q)}{5} - \frac{1}{2} \cdot - 6 = \frac{3}{5} q$

Step 2.1.4.3

Cancel the common factor.

$\frac{2 q}{5} + \frac{- 1}{2} \cdot \frac{2 q}{5} - \frac{1}{2} \cdot - 6 = \frac{3}{5} q$

Step 2.1.4.4

Rewrite the expression.

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

Step 2.1.5

Cancel the common factor of $2$ .

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Step 2.1.5.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{2 q}{5} - 1 \frac{q}{5} + \frac{- 1}{2} \cdot - 6 = \frac{3}{5} q$

Step 2.1.5.2

Factor $2$ out of $- 6$ .

$\frac{2 q}{5} - 1 \frac{q}{5} + \frac{- 1}{2} \cdot (2 (- 3)) = \frac{3}{5} q$

Step 2.1.5.3

Cancel the common factor.

$\frac{2 q}{5} - 1 \frac{q}{5} + \frac{- 1}{2} \cdot (2 \cdot - 3) = \frac{3}{5} q$

Step 2.1.5.4

Rewrite the expression.

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

Step 2.1.6

Multiply $- 1$ by $- 3$ .

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

Step 2.1.7

Rewrite $- 1 \frac{q}{5}$ as $- \frac{q}{5}$ .

$\frac{2 q}{5} - \frac{q}{5} + 3 = \frac{3}{5} q$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the numerators over the common denominator.

$3 + \frac{2 q - q}{5} = \frac{3}{5} q$

Step 2.2.2

Subtract $q$ from $2 q$ .

$3 + \frac{q}{5} = \frac{3}{5} q$

Step 3

Combine $\frac{3}{5}$ and $q$ .

$3 + \frac{q}{5} = \frac{3 q}{5}$

Step 4

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

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Step 4.1

Subtract $\frac{3 q}{5}$ from both sides of the equation.

$3 + \frac{q}{5} - \frac{3 q}{5} = 0$

Step 4.2

Combine the numerators over the common denominator.

$3 + \frac{q - 3 q}{5} = 0$

Step 4.3

Subtract $3 q$ from $q$ .

$3 + \frac{- 2 q}{5} = 0$

Step 4.4

Move the negative in front of the fraction.

$3 - \frac{2 q}{5} = 0$

Step 5

Subtract $3$ from both sides of the equation.

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

Step 6

Multiply both sides of the equation by $- \frac{5}{2}$ .

$- \frac{5}{2} (- \frac{2 q}{5}) = - \frac{5}{2} \cdot - 3$

Step 7

Simplify both sides of the equation.

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Step 7.1

Simplify the left side.

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Step 7.1.1

Simplify $- \frac{5}{2} (- \frac{2 q}{5})$ .

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Step 7.1.1.1

Cancel the common factor of $5$ .

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Step 7.1.1.1.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{- 5}{2} (- \frac{2 q}{5}) = - \frac{5}{2} \cdot - 3$

Step 7.1.1.1.2

Move the leading negative in $- \frac{2 q}{5}$ into the numerator.

$\frac{- 5}{2} \cdot \frac{- 2 q}{5} = - \frac{5}{2} \cdot - 3$

Step 7.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{2} \cdot \frac{- 2 q}{5} = - \frac{5}{2} \cdot - 3$

Step 7.1.1.1.4

Cancel the common factor.

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

Step 7.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} (- 2 q) = - \frac{5}{2} \cdot - 3$

Step 7.1.1.2

Cancel the common factor of $2$ .

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Step 7.1.1.2.1

Factor $2$ out of $- 2 q$ .

$\frac{- 1}{2} (2 (- q)) = - \frac{5}{2} \cdot - 3$

Step 7.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} (2 (- q)) = - \frac{5}{2} \cdot - 3$

Step 7.1.1.2.3

Rewrite the expression.

$- - q = - \frac{5}{2} \cdot - 3$

Step 7.1.1.3

Multiply.

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Step 7.1.1.3.1

Multiply $- 1$ by $- 1$ .

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

Step 7.1.1.3.2

Multiply $q$ by $1$ .

$q = - \frac{5}{2} \cdot - 3$

Step 7.2

Simplify the right side.

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Step 7.2.1

Multiply $- \frac{5}{2} \cdot - 3$ .

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Step 7.2.1.1

Multiply $- 3$ by $- 1$ .

$q = 3 (\frac{5}{2})$

Step 7.2.1.2

Combine $3$ and $\frac{5}{2}$ .

$q = \frac{3 \cdot 5}{2}$

Step 7.2.1.3

Multiply $3$ by $5$ .

$q = \frac{15}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$q = \frac{15}{2}$

Decimal Form:

$q = 7.5$

Mixed Number Form:

$q = 7 \frac{1}{2}$