Linear Algebra Examples

$5 (r - 8) = - 5 (r - 8)$

Step 1

Simplify $5 (r - 8)$ .

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Step 1.1

Rewrite.

$0 + 0 + 5 (r - 8) = - 5 (r - 8)$

Step 1.2

Simplify by adding zeros.

$5 (r - 8) = - 5 (r - 8)$

Step 1.3

Apply the distributive property.

$5 r + 5 \cdot - 8 = - 5 (r - 8)$

Step 1.4

Multiply $5$ by $- 8$ .

$5 r - 40 = - 5 (r - 8)$

Step 2

Simplify $- 5 (r - 8)$ .

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Step 2.1

Apply the distributive property.

$5 r - 40 = - 5 r - 5 \cdot - 8$

Step 2.2

Multiply $- 5$ by $- 8$ .

$5 r - 40 = - 5 r + 40$

Step 3

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

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Step 3.1

Add $5 r$ to both sides of the equation.

$5 r - 40 + 5 r = 40$

Step 3.2

Add $5 r$ and $5 r$ .

$10 r - 40 = 40$

Step 4

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

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Step 4.1

Add $40$ to both sides of the equation.

$10 r = 40 + 40$

Step 4.2

Add $40$ and $40$ .

$10 r = 80$

Step 5

Divide each term in $10 r = 80$ by $10$ and simplify.

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Step 5.1

Divide each term in $10 r = 80$ by $10$ .

$\frac{10 r}{10} = \frac{80}{10}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $10$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{10 r}{10} = \frac{80}{10}$

Step 5.2.1.2

Divide $r$ by $1$ .

$r = \frac{80}{10}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $80$ by $10$ .

$r = 8$

Step 6

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

${r | r = 8}$

Step 7