Basic Math Examples

$20 = \frac{5}{2 r} \cdot (r + 14)$

Step 1

Rewrite the equation as $\frac{5}{2 r} \cdot (r + 14) = 20$ .

$\frac{5}{2 r} \cdot (r + 14) = 20$

Step 2

Find the LCD of the terms in the equation.

Tap for more steps...

Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$2 r, 1, 1$

Step 2.2

The LCM of one and any expression is the expression.

$2 r$

Step 3

Multiply each term in $\frac{5}{2 r} \cdot (r + 14) = 20$ by $2 r$ to eliminate the fractions.

Tap for more steps...

Step 3.1

Multiply each term in $\frac{5}{2 r} \cdot (r + 14) = 20$ by $2 r$ .

$\frac{5}{2 r} \cdot (r + 14) (2 r) = 20 (2 r)$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Rewrite using the commutative property of multiplication.

$2 \frac{5}{2 r} (r + 14) r = 20 (2 r)$

Step 3.2.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.2.1

Factor $2$ out of $2 r$ .

$2 \frac{5}{2 (r)} (r + 14) r = 20 (2 r)$

Step 3.2.2.2

Cancel the common factor.

$2 \frac{5}{2 r} (r + 14) r = 20 (2 r)$

Step 3.2.2.3

Rewrite the expression.

$\frac{5}{r} (r + 14) r = 20 (2 r)$

Step 3.2.3

Multiply $\frac{5}{r}$ by $r + 14$ .

$\frac{5 (r + 14)}{r} r = 20 (2 r)$

Step 3.2.4

Cancel the common factor of $r$ .

Tap for more steps...

Step 3.2.4.1

Cancel the common factor.

$\frac{5 (r + 14)}{r} r = 20 (2 r)$

Step 3.2.4.2

Rewrite the expression.

$5 (r + 14) = 20 (2 r)$

Step 3.2.5

Apply the distributive property.

$5 r + 5 \cdot 14 = 20 (2 r)$

Step 3.2.6

Multiply $5$ by $14$ .

$5 r + 70 = 20 (2 r)$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Multiply $2$ by $20$ .

$5 r + 70 = 40 r$

Step 4

Solve the equation.

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Subtract $40 r$ from both sides of the equation.

$5 r + 70 - 40 r = 0$

Step 4.1.2

Subtract $40 r$ from $5 r$ .

$- 35 r + 70 = 0$

Step 4.2

Subtract $70$ from both sides of the equation.

$- 35 r = - 70$

Step 4.3

Divide each term in $- 35 r = - 70$ by $- 35$ and simplify.

Tap for more steps...

Step 4.3.1

Divide each term in $- 35 r = - 70$ by $- 35$ .

$\frac{- 35 r}{- 35} = \frac{- 70}{- 35}$

Step 4.3.2

Simplify the left side.

Tap for more steps...

Step 4.3.2.1

Cancel the common factor of $- 35$ .

Tap for more steps...

Step 4.3.2.1.1

Cancel the common factor.

$\frac{- 35 r}{- 35} = \frac{- 70}{- 35}$

Step 4.3.2.1.2

Divide $r$ by $1$ .

$r = \frac{- 70}{- 35}$

Step 4.3.3

Simplify the right side.

Tap for more steps...

Step 4.3.3.1

Divide $- 70$ by $- 35$ .

$r = 2$