Find the Product 1/2(2/3e-3+2e)=-4(1/8e+1-e)

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

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.

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

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

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.

Multiply $3$ by $2$ .

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

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.

Apply the distributive property.

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

Simplify terms.

Cancel the common factor of $2$ .

Factor $2$ out of $8 e$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Move the negative in front of the fraction.

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

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.

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

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

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.

Simplify the numerator.

Multiply $8$ by $- 1$ .

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

Subtract $8 e$ from $e$ .

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

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.

Apply the distributive property.

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

Cancel the common factor of $4$ .

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

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

Factor $4$ out of $- 4$ .

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

Factor $4$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $- 4$ by $1$ .

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

Step 10

Simplify each term.

Move the negative in front of the fraction.

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

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

Multiply $- 1$ by $- 1$ .

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

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

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

Find the Product 1/2(2/3e-3+2e)=-4(1/8e+1-e)

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