Linear Algebra Examples

$\frac{1}{3} \cdot (c - 2) = \frac{7}{3}$

Step 1

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} \cdot (c - 2)) = 3 (\frac{7}{3})$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $3 (\frac{1}{3} \cdot (c - 2))$ .

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Step 2.1.1.1

Apply the distributive property.

$3 (\frac{1}{3} c + \frac{1}{3} \cdot - 2) = 3 (\frac{7}{3})$

Step 2.1.1.2

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

$3 (\frac{c}{3} + \frac{1}{3} \cdot - 2) = 3 (\frac{7}{3})$

Step 2.1.1.3

Combine $\frac{1}{3}$ and $- 2$ .

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

Step 2.1.1.4

Move the negative in front of the fraction.

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

Step 2.1.1.5

Apply the distributive property.

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

Step 2.1.1.6

Cancel the common factor of $3$ .

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Step 2.1.1.6.1

Cancel the common factor.

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

Step 2.1.1.6.2

Rewrite the expression.

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

Step 2.1.1.7

Cancel the common factor of $3$ .

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Step 2.1.1.7.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

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

Step 2.1.1.7.2

Cancel the common factor.

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

Step 2.1.1.7.3

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Rewrite the expression.

$c - 2 = 7$

Step 3

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

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Step 3.1

Add $2$ to both sides of the equation.

$c = 7 + 2$

Step 3.2

Add $7$ and $2$ .

$c = 9$

Step 4

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

${c | c = 9}$

Step 5