Algebra Examples

$\frac{1}{5} (\frac{3}{2} d - 15) = \frac{9}{10} d$

Step 1

Simplify $\frac{1}{5} \cdot (\frac{3}{2} d - 15)$ .

Tap for more steps...

Step 1.1

Rewrite.

$0 + 0 + \frac{1}{5} \cdot (\frac{3}{2} d - 15) = \frac{9}{10} d$

Step 1.2

Simplify by adding zeros.

$\frac{1}{5} \cdot (\frac{3}{2} d - 15) = \frac{9}{10} d$

Step 1.3

Combine $\frac{3}{2}$ and $d$ .

$\frac{1}{5} \cdot (\frac{3 d}{2} - 15) = \frac{9}{10} d$

Step 1.4

Apply the distributive property.

$\frac{1}{5} \cdot \frac{3 d}{2} + \frac{1}{5} \cdot - 15 = \frac{9}{10} d$

Step 1.5

Multiply $\frac{1}{5} \cdot \frac{3 d}{2}$ .

Tap for more steps...

Step 1.5.1

Multiply $\frac{1}{5}$ by $\frac{3 d}{2}$ .

$\frac{3 d}{5 \cdot 2} + \frac{1}{5} \cdot - 15 = \frac{9}{10} d$

Step 1.5.2

Multiply $5$ by $2$ .

$\frac{3 d}{10} + \frac{1}{5} \cdot - 15 = \frac{9}{10} d$

Step 1.6

Cancel the common factor of $5$ .

Tap for more steps...

Step 1.6.1

Factor $5$ out of $- 15$ .

$\frac{3 d}{10} + \frac{1}{5} \cdot (5 (- 3)) = \frac{9}{10} d$

Step 1.6.2

Cancel the common factor.

$\frac{3 d}{10} + \frac{1}{5} \cdot (5 \cdot - 3) = \frac{9}{10} d$

Step 1.6.3

Rewrite the expression.

$\frac{3 d}{10} - 3 = \frac{9}{10} d$

Step 2

Combine $\frac{9}{10}$ and $d$ .

$\frac{3 d}{10} - 3 = \frac{9 d}{10}$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $\frac{9 d}{10}$ from both sides of the equation.

$\frac{3 d}{10} - 3 - \frac{9 d}{10} = 0$

Step 3.2

Combine the numerators over the common denominator.

$- 3 + \frac{3 d - 9 d}{10} = 0$

Step 3.3

Subtract $9 d$ from $3 d$ .

$- 3 + \frac{- 6 d}{10} = 0$

Step 3.4

Simplify each term.

Tap for more steps...

Step 3.4.1

Cancel the common factor of $- 6$ and $10$ .

Tap for more steps...

Step 3.4.1.1

Factor $2$ out of $- 6 d$ .

$- 3 + \frac{2 (- 3 d)}{10} = 0$

Step 3.4.1.2

Cancel the common factors.

Tap for more steps...

Step 3.4.1.2.1

Factor $2$ out of $10$ .

$- 3 + \frac{2 (- 3 d)}{2 (5)} = 0$

Step 3.4.1.2.2

Cancel the common factor.

$- 3 + \frac{2 (- 3 d)}{2 \cdot 5} = 0$

Step 3.4.1.2.3

Rewrite the expression.

$- 3 + \frac{- 3 d}{5} = 0$

Step 3.4.2

Move the negative in front of the fraction.

$- 3 - \frac{3 d}{5} = 0$

Step 4

Add $3$ to both sides of the equation.

$- \frac{3 d}{5} = 3$

Step 5

Multiply both sides of the equation by $- \frac{5}{3}$ .

$- \frac{5}{3} (- \frac{3 d}{5}) = - \frac{5}{3} \cdot 3$

Step 6

Simplify both sides of the equation.

Tap for more steps...

Step 6.1

Simplify the left side.

Tap for more steps...

Step 6.1.1

Simplify $- \frac{5}{3} (- \frac{3 d}{5})$ .

Tap for more steps...

Step 6.1.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 6.1.1.1.1

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$\frac{- 5}{3} (- \frac{3 d}{5}) = - \frac{5}{3} \cdot 3$

Step 6.1.1.1.2

Move the leading negative in $- \frac{3 d}{5}$ into the numerator.

$\frac{- 5}{3} \cdot \frac{- 3 d}{5} = - \frac{5}{3} \cdot 3$

Step 6.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{3} \cdot \frac{- 3 d}{5} = - \frac{5}{3} \cdot 3$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{3} \cdot \frac{- 3 d}{5} = - \frac{5}{3} \cdot 3$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 d) = - \frac{5}{3} \cdot 3$

Step 6.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.1.1.2.1

Factor $3$ out of $- 3 d$ .

$\frac{- 1}{3} (3 (- d)) = - \frac{5}{3} \cdot 3$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- d)) = - \frac{5}{3} \cdot 3$

Step 6.1.1.2.3

Rewrite the expression.

$- - d = - \frac{5}{3} \cdot 3$

Step 6.1.1.3

Multiply.

Tap for more steps...

Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 d = - \frac{5}{3} \cdot 3$

Step 6.1.1.3.2

Multiply $d$ by $1$ .

$d = - \frac{5}{3} \cdot 3$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.2.1.1

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$d = \frac{- 5}{3} \cdot 3$

Step 6.2.1.2

Cancel the common factor.

$d = \frac{- 5}{3} \cdot 3$

Step 6.2.1.3

Rewrite the expression.

$d = - 5$