How to solve N = 1/2 + I * 2/L

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve N = 1/2 + I * 2/L | Equatix

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Question

$$N=\frac{1}{2}+I\frac{2}{L}$$

Solve for I

$I=\frac{L\left(2N-1\right)}{4}$
$L\neq 0$

Steps for Solving Linear Equation

Multiply both sides of the equation by $2L$, the least common multiple of $2,L$.

$$N\times 2L=2L\times \frac{1}{2}+I\times 2\times 2$$

Multiply $2$ and $\frac{1}{2}$ to get $1$.

$$N\times 2L=L+I\times 2\times 2$$

Multiply $2$ and $2$ to get $4$.

$$N\times 2L=L+I\times 4$$

Swap sides so that all variable terms are on the left hand side.

$$L+I\times 4=N\times 2L$$

Subtract $L$ from both sides.

$$I\times 4=N\times 2L-L$$

The equation is in standard form.

$$4I=2LN-L$$

Divide both sides by $4$.

$$\frac{4I}{4}=\frac{L\left(2N-1\right)}{4}$$

Dividing by $4$ undoes the multiplication by $4$.

$$I=\frac{L\left(2N-1\right)}{4}$$

Divide $L\left(-1+2N\right)$ by $4$.

$$I=\frac{LN}{2}-\frac{L}{4}$$

Show Solution

Solve for L

$\left\{\begin{matrix}L=-\frac{4I}{1-2N}\text{, }&I\neq 0\text{ and }N\neq \frac{1}{2}\\L\neq 0\text{, }&N=\frac{1}{2}\text{ and }I=0\end{matrix}\right.$

Steps for Solving Linear Equation

Variable $L$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $2L$, the least common multiple of $2,L$.

$$N\times 2L=2L\times \frac{1}{2}+I\times 2\times 2$$

Multiply $2$ and $\frac{1}{2}$ to get $1$.

$$N\times 2L=L+I\times 2\times 2$$

Multiply $2$ and $2$ to get $4$.

$$N\times 2L=L+I\times 4$$

Subtract $L$ from both sides.

$$N\times 2L-L=I\times 4$$

Combine all terms containing $L$.

$$\left(N\times 2-1\right)L=I\times 4$$

The equation is in standard form.

$$\left(2N-1\right)L=4I$$

Divide both sides by $2N-1$.

$$\frac{\left(2N-1\right)L}{2N-1}=\frac{4I}{2N-1}$$

Dividing by $2N-1$ undoes the multiplication by $2N-1$.

$$L=\frac{4I}{2N-1}$$

Variable $L$ cannot be equal to $0$.

$$L=\frac{4I}{2N-1}\text{, }L\neq 0$$

Show Solution

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Example

Question

Solve for I

Steps for Solving Linear Equation

Solve for L

Steps for Solving Linear Equation