Algebra Examples

$\frac{1}{2} (\frac{2}{3} e - 3 + 2 e) = - 4 (\frac{1}{8} e + 1 - e)$

Step 1

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

$\frac{1}{2} \cdot (\frac{2 e}{3} - 3 + 2 e) = - 4 (\frac{1}{8} \cdot e + 1 - e)$

Step 2

To write $2 e$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{2} \cdot (\frac{2 e}{3} + 2 e \cdot \frac{3}{3} - 3) = - 4 (\frac{1}{8} \cdot e + 1 - e)$

Step 3

Combine fractions.

Tap for more steps...

Step 3.1

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

$\frac{1}{2} \cdot (\frac{2 e}{3} + \frac{2 e \cdot 3}{3} - 3) = - 4 (\frac{1}{8} \cdot e + 1 - e)$

Step 3.2

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot (\frac{2 e + 2 e \cdot 3}{3} - 3) = - 4 (\frac{1}{8} \cdot e + 1 - e)$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Multiply $3$ by $2$ .

$\frac{1}{2} \cdot (\frac{2 e + 6 e}{3} - 3) = - 4 (\frac{1}{8} \cdot e + 1 - e)$

Step 4.2

Add $2 e$ and $6 e$ .

$\frac{1}{2} \cdot (\frac{8 e}{3} - 3) = - 4 (\frac{1}{8} \cdot e + 1 - e)$

Step 5

Simplify terms.

Tap for more steps...

Step 5.1

Apply the distributive property.

$\frac{1}{2} \cdot \frac{8 e}{3} + \frac{1}{2} \cdot - 3 = - 4 (\frac{1}{8} \cdot e + 1 - e)$

Step 5.2

Simplify terms.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.2.1.1

Factor $2$ out of $8 e$ .

$\frac{1}{2} \cdot \frac{2 (4 e)}{3} + \frac{1}{2} \cdot - 3 = - 4 (\frac{1}{8} \cdot e + 1 - e)$

Step 5.2.1.2

Cancel the common factor.

$\frac{1}{2} \cdot \frac{2 (4 e)}{3} + \frac{1}{2} \cdot - 3 = - 4 (\frac{1}{8} \cdot e + 1 - e)$

Step 5.2.1.3

Rewrite the expression.

$\frac{4 e}{3} + \frac{1}{2} \cdot - 3 = - 4 (\frac{1}{8} \cdot e + 1 - e)$

Step 5.2.2

Combine $\frac{1}{2}$ and $- 3$ .

$\frac{4 e}{3} + \frac{- 3}{2} = - 4 (\frac{1}{8} \cdot e + 1 - e)$

Step 5.2.3

Move the negative in front of the fraction.

$\frac{4 e}{3} - \frac{3}{2} = - 4 (\frac{1}{8} \cdot e + 1 - e)$

Step 5.3

Combine $\frac{1}{8}$ and $e$ .

$\frac{4 e}{3} - \frac{3}{2} = - 4 (\frac{e}{8} + 1 - e)$

Step 6

To write $- e$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{4 e}{3} - \frac{3}{2} = - 4 (\frac{e}{8} - e \cdot \frac{8}{8} + 1)$

Step 7

Combine fractions.

Tap for more steps...

Step 7.1

Combine $- e$ and $\frac{8}{8}$ .

$\frac{4 e}{3} - \frac{3}{2} = - 4 (\frac{e}{8} + \frac{- e \cdot 8}{8} + 1)$

Step 7.2

Combine the numerators over the common denominator.

$\frac{4 e}{3} - \frac{3}{2} = - 4 (\frac{e - e \cdot 8}{8} + 1)$

Step 8

Simplify each term.

Tap for more steps...

Step 8.1

Simplify the numerator.

Tap for more steps...

Step 8.1.1

Multiply $8$ by $- 1$ .

$\frac{4 e}{3} - \frac{3}{2} = - 4 (\frac{e - 8 e}{8} + 1)$

Step 8.1.2

Subtract $8 e$ from $e$ .

$\frac{4 e}{3} - \frac{3}{2} = - 4 (\frac{- 7 e}{8} + 1)$

Step 8.2

Move the negative in front of the fraction.

$\frac{4 e}{3} - \frac{3}{2} = - 4 (- \frac{7 e}{8} + 1)$

Step 9

Simplify terms.

Tap for more steps...

Step 9.1

Apply the distributive property.

$\frac{4 e}{3} - \frac{3}{2} = - 4 (- \frac{7 e}{8}) - 4 \cdot 1$

Step 9.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 9.2.1

Move the leading negative in $- \frac{7 e}{8}$ into the numerator.

$\frac{4 e}{3} - \frac{3}{2} = - 4 \frac{- 7 e}{8} - 4 \cdot 1$

Step 9.2.2

Factor $4$ out of $- 4$ .

$\frac{4 e}{3} - \frac{3}{2} = 4 (- 1) \frac{- 7 e}{8} - 4 \cdot 1$

Step 9.2.3

Factor $4$ out of $8$ .

$\frac{4 e}{3} - \frac{3}{2} = 4 \cdot - 1 \frac{- 7 e}{4 \cdot 2} - 4 \cdot 1$

Step 9.2.4

Cancel the common factor.

$\frac{4 e}{3} - \frac{3}{2} = 4 \cdot - 1 \frac{- 7 e}{4 \cdot 2} - 4 \cdot 1$

Step 9.2.5

Rewrite the expression.

$\frac{4 e}{3} - \frac{3}{2} = - 1 \frac{- 7 e}{2} - 4 \cdot 1$

Step 9.3

Multiply $- 4$ by $1$ .

$\frac{4 e}{3} - \frac{3}{2} = - 1 \frac{- 7 e}{2} - 4$

Step 10

Simplify each term.

Tap for more steps...

Step 10.1

Move the negative in front of the fraction.

$\frac{4 e}{3} - \frac{3}{2} = - 1 (- \frac{7 e}{2}) - 4$

Step 10.2

Multiply $- 1 (- \frac{7 e}{2})$ .

Tap for more steps...

Step 10.2.1

Multiply $- 1$ by $- 1$ .

$\frac{4 e}{3} - \frac{3}{2} = 1 \frac{7 e}{2} - 4$

Step 10.2.2

Multiply $\frac{7 e}{2}$ by $1$ .

$\frac{4 e}{3} - \frac{3}{2} = \frac{7 e}{2} - 4$