Algebra Examples

$\frac{1}{3} q + \frac{2}{3} = \frac{8}{3} q - \frac{5}{3}$

Step 1

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

$\frac{q}{3} + \frac{2}{3} = \frac{8}{3} q - \frac{5}{3}$

Step 2

Combine $\frac{8}{3}$ and $q$ .

$\frac{q}{3} + \frac{2}{3} = \frac{8 q}{3} - \frac{5}{3}$

Step 3

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

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Step 3.1

Subtract $\frac{8 q}{3}$ from both sides of the equation.

$\frac{q}{3} + \frac{2}{3} - \frac{8 q}{3} = - \frac{5}{3}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{q + 2 - 8 q}{3} = - \frac{5}{3}$

Step 3.3

Subtract $8 q$ from $q$ .

$\frac{- 7 q + 2}{3} = - \frac{5}{3}$

Step 3.4

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

$\frac{- (7 q) + 2}{3} = - \frac{5}{3}$

Step 3.5

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{- (7 q) - 1 (- 2)}{3} = - \frac{5}{3}$

Step 3.6

Factor $- 1$ out of $- (7 q) - 1 (- 2)$ .

$\frac{- (7 q - 2)}{3} = - \frac{5}{3}$

Step 3.7

Rewrite $- (7 q - 2)$ as $- 1 (7 q - 2)$ .

$\frac{- 1 (7 q - 2)}{3} = - \frac{5}{3}$

Step 3.8

Move the negative in front of the fraction.

$- \frac{7 q - 2}{3} = - \frac{5}{3}$

Step 4

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

$- (7 q - 2) = - 5$

Step 5

Simplify $- (7 q - 2)$ .

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Step 5.1

Apply the distributive property.

$- (7 q) - - 2 = - 5$

Step 5.2

Multiply.

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Step 5.2.1

Multiply $7$ by $- 1$ .

$- 7 q - - 2 = - 5$

Step 5.2.2

Multiply $- 1$ by $- 2$ .

$- 7 q + 2 = - 5$

Step 6

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

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Step 6.1

Subtract $2$ from both sides of the equation.

$- 7 q = - 5 - 2$

Step 6.2

Subtract $2$ from $- 5$ .

$- 7 q = - 7$

Step 7

Divide each term in $- 7 q = - 7$ by $- 7$ and simplify.

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Step 7.1

Divide each term in $- 7 q = - 7$ by $- 7$ .

$\frac{- 7 q}{- 7} = \frac{- 7}{- 7}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $- 7$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{- 7 q}{- 7} = \frac{- 7}{- 7}$

Step 7.2.1.2

Divide $q$ by $1$ .

$q = \frac{- 7}{- 7}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Divide $- 7$ by $- 7$ .

$q = 1$