Solve M = 1 + 7/(2 - 1/n) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$M=1+\frac{7}{2-\frac{1}{n}}$$

Solve for n

$n=-\frac{M-1}{9-2M}$
$M\neq \frac{9}{2}\text{ and }M\neq 1$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply $2$ times $\frac{n}{n}$.

$$M=1+\frac{7}{\frac{2n}{n}-\frac{1}{n}}$$

Since $\frac{2n}{n}$ and $\frac{1}{n}$ have the same denominator, subtract them by subtracting their numerators.

$$M=1+\frac{7}{\frac{2n-1}{n}}$$

Variable $n$ cannot be equal to $0$ since division by zero is not defined. Divide $7$ by $\frac{2n-1}{n}$ by multiplying $7$ by the reciprocal of $\frac{2n-1}{n}$.

$$M=1+\frac{7n}{2n-1}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $1$ times $\frac{2n-1}{2n-1}$.

$$M=\frac{2n-1}{2n-1}+\frac{7n}{2n-1}$$

Since $\frac{2n-1}{2n-1}$ and $\frac{7n}{2n-1}$ have the same denominator, add them by adding their numerators.

$$M=\frac{2n-1+7n}{2n-1}$$

Combine like terms in $2n-1+7n$.

$$M=\frac{9n-1}{2n-1}$$

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

$$\frac{9n-1}{2n-1}=M$$

Variable $n$ cannot be equal to $\frac{1}{2}$ since division by zero is not defined. Multiply both sides of the equation by $2n-1$.

$$9n-1=M\left(2n-1\right)$$

Use the distributive property to multiply $M$ by $2n-1$.

$$9n-1=2Mn-M$$

Subtract $2Mn$ from both sides.

$$9n-1-2Mn=-M$$

Add $1$ to both sides.

$$9n-2Mn=-M+1$$

Combine all terms containing $n$.

$$\left(9-2M\right)n=-M+1$$

The equation is in standard form.

$$\left(9-2M\right)n=1-M$$

Divide both sides by $9-2M$.

$$\frac{\left(9-2M\right)n}{9-2M}=\frac{1-M}{9-2M}$$

Dividing by $9-2M$ undoes the multiplication by $9-2M$.

$$n=\frac{1-M}{9-2M}$$

Variable $n$ cannot be equal to any of the values $\frac{1}{2},0$.

$$n=\frac{1-M}{9-2M}\text{, }n\neq \frac{1}{2}\text{ and }n\neq 0$$

Solve for M

$M=-\frac{1-9n}{2n-1}$
$n\neq \frac{1}{2}\text{ and }n\neq 0$