Solve ell=5+(n-1)d

$$\ell = 5 + ( n - 1 ) d$$

Solve for d

$$\left\{\begin{matrix}d=-\frac{5-ℓ}{n-1}\text{, }&n\neq 1\\d\in \mathrm{R}\text{, }&ℓ=5\text{ and }n=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-1 by d.

$$ℓ=5+nd-d$$

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

$$5+nd-d=ℓ$$

Subtract 5 from both sides.

$$nd-d=ℓ-5$$

Combine all terms containing d.

$$\left(n-1\right)d=ℓ-5$$

Divide both sides by n-1.

$$\frac{\left(n-1\right)d}{n-1}=\frac{ℓ-5}{n-1}$$

Dividing by n-1 undoes the multiplication by n-1.

$$d=\frac{ℓ-5}{n-1}$$

Solve for n

$$\left\{\begin{matrix}n=\frac{d+ℓ-5}{d}\text{, }&d\neq 0\\n\in \mathrm{R}\text{, }&ℓ=5\text{ and }d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply n-1 by d.

$$ℓ=5+nd-d$$

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

$$5+nd-d=ℓ$$

Subtract 5 from both sides.

$$nd-d=ℓ-5$$

Add d to both sides.

$$nd=ℓ-5+d$$

The equation is in standard form.

$$dn=d+ℓ-5$$

Divide both sides by d.

$$\frac{dn}{d}=\frac{d+ℓ-5}{d}$$

Dividing by d undoes the multiplication by d.

$$n=\frac{d+ℓ-5}{d}$$