Basic Math Examples

$- 4 = \frac{- 11 - r}{2 - (- 5)}$

Step 1

Rewrite the equation as $\frac{- 11 - r}{2 - (- 5)} = - 4$ .

$\frac{- 11 - r}{2 - (- 5)} = - 4$

Step 2

Multiply both sides by $2 - (- 5)$ .

$\frac{- 11 - r}{2 - (- 5)} (2 - (- 5)) = - 4 (2 - (- 5))$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{- 11 - r}{2 - (- 5)} (2 - (- 5))$ .

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Step 3.1.1.1

Cancel the common factor of $2 - - 5$ .

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Step 3.1.1.1.1

Multiply by $1$ .

$\frac{- 11 - r}{(2 - (- 5)) \cdot 1} (2 - (- 5)) = - 4 (2 - (- 5))$

Step 3.1.1.1.2

Multiply by $1$ .

$\frac{- 11 - r}{(2 - (- 5)) \cdot 1} ((2 - (- 5)) \cdot 1) = - 4 (2 - (- 5))$

Step 3.1.1.1.3

Rewrite the expression.

$- 11 - r = - 4 (2 - (- 5))$

Step 3.1.1.2

Reorder $- 11$ and $- r$ .

$- r - 11 = - 4 (2 - (- 5))$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- 4 (2 - (- 5))$ .

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Step 3.2.1.1

Multiply $- 1$ by $- 5$ .

$- r - 11 = - 4 (2 + 5)$

Step 3.2.1.2

Add $2$ and $5$ .

$- r - 11 = - 4 \cdot 7$

Step 3.2.1.3

Multiply $- 4$ by $7$ .

$- r - 11 = - 28$

Step 4

Solve for $r$ .

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Step 4.1

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

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Step 4.1.1

Add $11$ to both sides of the equation.

$- r = - 28 + 11$

Step 4.1.2

Add $- 28$ and $11$ .

$- r = - 17$

Step 4.2

Divide each term in $- r = - 17$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- r = - 17$ by $- 1$ .

$\frac{- r}{- 1} = \frac{- 17}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{r}{1} = \frac{- 17}{- 1}$

Step 4.2.2.2

Divide $r$ by $1$ .

$r = \frac{- 17}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 17$ by $- 1$ .

$r = 17$