Solve for j 3/4j-2(1/2j+2)=1/8j

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

Step 1

Simplify $\frac{3}{4} j - 2 (\frac{1}{2} j + 2)$ .

Simplify each term.

Combine $\frac{3}{4}$ and $j$ .

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

Combine $\frac{1}{2}$ and $j$ .

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

$\frac{3 j}{4} + 2 \cdot - 1 \frac{j}{2} - 2 \cdot 2 = \frac{1}{8} j$

Rewrite the expression.

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

Multiply $- 2$ by $2$ .

$\frac{3 j}{4} - 1 j - 4 = \frac{1}{8} j$

Rewrite $- 1 j$ as $- j$ .

$\frac{3 j}{4} - j - 4 = \frac{1}{8} j$

To write $- j$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 j}{4} - j \cdot \frac{4}{4} - 4 = \frac{1}{8} j$

Simplify terms.

Combine $- j$ and $\frac{4}{4}$ .

$\frac{3 j}{4} + \frac{- j \cdot 4}{4} - 4 = \frac{1}{8} j$

Combine the numerators over the common denominator.

$\frac{3 j - j \cdot 4}{4} - 4 = \frac{1}{8} j$

Simplify each term.

Simplify the numerator.

Factor $j$ out of $3 j - j \cdot 4$ .

Factor $j$ out of $3 j$ .

$\frac{j \cdot 3 - j \cdot 4}{4} - 4 = \frac{1}{8} j$

Factor $j$ out of $- j \cdot 4$ .

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

Factor $j$ out of $j \cdot 3 + j (- 1 \cdot 4)$ .

$\frac{j (3 - 1 \cdot 4)}{4} - 4 = \frac{1}{8} j$

Multiply $- 1$ by $4$ .

$\frac{j (3 - 4)}{4} - 4 = \frac{1}{8} j$

Subtract $4$ from $3$ .

$\frac{j \cdot - 1}{4} - 4 = \frac{1}{8} j$

Move $- 1$ to the left of $j$ .

$\frac{- 1 \cdot j}{4} - 4 = \frac{1}{8} j$

Move the negative in front of the fraction.

$- \frac{j}{4} - 4 = \frac{1}{8} j$

Step 2

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

$- \frac{j}{4} - 4 = \frac{j}{8}$

Step 3

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

Subtract $\frac{j}{8}$ from both sides of the equation.

$- \frac{j}{4} - 4 - \frac{j}{8} = 0$

To write $- \frac{j}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{j}{4} \cdot \frac{2}{2} - \frac{j}{8} - 4 = 0$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{j}{4}$ by $\frac{2}{2}$ .

$- \frac{j \cdot 2}{4 \cdot 2} - \frac{j}{8} - 4 = 0$

Multiply $4$ by $2$ .

$- \frac{j \cdot 2}{8} - \frac{j}{8} - 4 = 0$

Combine the numerators over the common denominator.

$\frac{- j \cdot 2 - j}{8} - 4 = 0$

Simplify each term.

Simplify the numerator.

Factor $j$ out of $- j \cdot 2 - j$ .

Factor $j$ out of $- j \cdot 2$ .

$\frac{j (- 1 \cdot 2) - j}{8} - 4 = 0$

Factor $j$ out of $- j$ .

$\frac{j (- 1 \cdot 2) + j \cdot - 1}{8} - 4 = 0$

Factor $j$ out of $j (- 1 \cdot 2) + j \cdot - 1$ .

$\frac{j (- 1 \cdot 2 - 1)}{8} - 4 = 0$

Multiply $- 1$ by $2$ .

$\frac{j (- 2 - 1)}{8} - 4 = 0$

Subtract $1$ from $- 2$ .

$\frac{j \cdot - 3}{8} - 4 = 0$

Move $- 3$ to the left of $j$ .

$\frac{- 3 \cdot j}{8} - 4 = 0$

Move the negative in front of the fraction.

$- \frac{3 j}{8} - 4 = 0$

Step 4

Add $4$ to both sides of the equation.

$- \frac{3 j}{8} = 4$

Step 5

Multiply both sides of the equation by $- \frac{8}{3}$ .

$- \frac{8}{3} (- \frac{3 j}{8}) = - \frac{8}{3} \cdot 4$

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{8}{3} (- \frac{3 j}{8})$ .

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{8}{3}$ into the numerator.

$\frac{- 8}{3} (- \frac{3 j}{8}) = - \frac{8}{3} \cdot 4$

Move the leading negative in $- \frac{3 j}{8}$ into the numerator.

$\frac{- 8}{3} \cdot \frac{- 3 j}{8} = - \frac{8}{3} \cdot 4$

Factor $8$ out of $- 8$ .

$\frac{8 (- 1)}{3} \cdot \frac{- 3 j}{8} = - \frac{8}{3} \cdot 4$

Cancel the common factor.

$\frac{8 \cdot - 1}{3} \cdot \frac{- 3 j}{8} = - \frac{8}{3} \cdot 4$

Rewrite the expression.

$\frac{- 1}{3} (- 3 j) = - \frac{8}{3} \cdot 4$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3 j$ .

$\frac{- 1}{3} (3 (- j)) = - \frac{8}{3} \cdot 4$

Cancel the common factor.

$\frac{- 1}{3} (3 (- j)) = - \frac{8}{3} \cdot 4$

Rewrite the expression.

$- - j = - \frac{8}{3} \cdot 4$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 j = - \frac{8}{3} \cdot 4$

Multiply $j$ by $1$ .

$j = - \frac{8}{3} \cdot 4$

Simplify the right side.

Simplify $- \frac{8}{3} \cdot 4$ .

Multiply $- \frac{8}{3} \cdot 4$ .

Multiply $4$ by $- 1$ .

$j = - 4 (\frac{8}{3})$

Combine $- 4$ and $\frac{8}{3}$ .

$j = \frac{- 4 \cdot 8}{3}$

Multiply $- 4$ by $8$ .

$j = \frac{- 32}{3}$

Move the negative in front of the fraction.

$j = - \frac{32}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$j = - \frac{32}{3}$

Decimal Form:

$j = - 10.\overline{6}$

Mixed Number Form:

$j = - 10 \frac{2}{3}$

Solve for j 3/4j-2(1/2j+2)=1/8j

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