Algebra Examples

$5 (r - 1) = 2 (r - 4) - 6$

Step 1

Simplify $5 (r - 1)$ .

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Step 1.1

Rewrite.

$0 + 0 + 5 (r - 1) = 2 (r - 4) - 6$

Step 1.2

Simplify by adding zeros.

$5 (r - 1) = 2 (r - 4) - 6$

Step 1.3

Apply the distributive property.

$5 r + 5 \cdot - 1 = 2 (r - 4) - 6$

Step 1.4

Multiply $5$ by $- 1$ .

$5 r - 5 = 2 (r - 4) - 6$

Step 2

Simplify $2 (r - 4) - 6$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$5 r - 5 = 2 r + 2 \cdot - 4 - 6$

Step 2.1.2

Multiply $2$ by $- 4$ .

$5 r - 5 = 2 r - 8 - 6$

Step 2.2

Subtract $6$ from $- 8$ .

$5 r - 5 = 2 r - 14$

Step 3

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

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Step 3.1

Subtract $2 r$ from both sides of the equation.

$5 r - 5 - 2 r = - 14$

Step 3.2

Subtract $2 r$ from $5 r$ .

$3 r - 5 = - 14$

Step 4

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

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Step 4.1

Add $5$ to both sides of the equation.

$3 r = - 14 + 5$

Step 4.2

Add $- 14$ and $5$ .

$3 r = - 9$

Step 5

Divide each term in $3 r = - 9$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 r = - 9$ by $3$ .

$\frac{3 r}{3} = \frac{- 9}{3}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 r}{3} = \frac{- 9}{3}$

Step 5.2.1.2

Divide $r$ by $1$ .

$r = \frac{- 9}{3}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 9$ by $3$ .

$r = - 3$