Linear Algebra Examples

$\frac{3 q - 2}{5} = - 4$

Step 1

Multiply both sides by $5$ .

$\frac{3 q - 2}{5} \cdot 5 = - 4 \cdot 5$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $5$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{3 q - 2}{5} \cdot 5 = - 4 \cdot 5$

Step 2.1.1.2

Rewrite the expression.

$3 q - 2 = - 4 \cdot 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 4$ by $5$ .

$3 q - 2 = - 20$

Step 3

Solve for $q$ .

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Step 3.1

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

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Step 3.1.1

Add $2$ to both sides of the equation.

$3 q = - 20 + 2$

Step 3.1.2

Add $- 20$ and $2$ .

$3 q = - 18$

Step 3.2

Divide each term in $3 q = - 18$ by $3$ and simplify.

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Step 3.2.1

Divide each term in $3 q = - 18$ by $3$ .

$\frac{3 q}{3} = \frac{- 18}{3}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{3 q}{3} = \frac{- 18}{3}$

Step 3.2.2.1.2

Divide $q$ by $1$ .

$q = \frac{- 18}{3}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 18$ by $3$ .

$q = - 6$

Step 4

The domain is the set of all valid $q$ values.

${q | q = - 6}$

Step 5