Solve for j -1/4j=2-3/4+1/2j+3/2j

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

Step 1

Since $j$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 2

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

Simplify each term.

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

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

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

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

Simplify terms.

Combine the numerators over the common denominator.

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

Add $j$ and $3 j$ .

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

Simplify each term.

Move the negative in front of the fraction.

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

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 j$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 j$ by $1$ .

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

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

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

Combine $2$ and $\frac{4}{4}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $4$ .

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

Subtract $3$ from $8$ .

$\frac{5}{4} + 2 j = - \frac{1}{4} j$

Step 3

Combine $j$ and $\frac{1}{4}$ .

$\frac{5}{4} + 2 j = - \frac{j}{4}$

Step 4

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

Add $\frac{j}{4}$ to both sides of the equation.

$\frac{5}{4} + 2 j + \frac{j}{4} = 0$

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

$\frac{5}{4} + 2 j \cdot \frac{4}{4} + \frac{j}{4} = 0$

Combine $2 j$ and $\frac{4}{4}$ .

$\frac{5}{4} + \frac{2 j \cdot 4}{4} + \frac{j}{4} = 0$

Combine the numerators over the common denominator.

$\frac{5}{4} + \frac{2 j \cdot 4 + j}{4} = 0$

Combine the numerators over the common denominator.

$\frac{5 + 2 j \cdot 4 + j}{4} = 0$

Multiply $4$ by $2$ .

$\frac{5 + 8 j + j}{4} = 0$

Add $8 j$ and $j$ .

$\frac{5 + 9 j}{4} = 0$

Step 5

Set the numerator equal to zero.

$5 + 9 j = 0$

Step 6

Solve the equation for $j$ .

Subtract $5$ from both sides of the equation.

$9 j = - 5$

Divide each term in $9 j = - 5$ by $9$ and simplify.

Divide each term in $9 j = - 5$ by $9$ .

$\frac{9 j}{9} = \frac{- 5}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 j}{9} = \frac{- 5}{9}$

Divide $j$ by $1$ .

$j = \frac{- 5}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$j = - \frac{5}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$j = - \frac{5}{9}$

Decimal Form:

$j = - 0.\overline{5}$

Solve for j -1/4j=2-3/4+1/2j+3/2j

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