Solve 3p(b+3)=m+1

$$3 p ( b + 3 ) = m + 1$$

Solve for b

$$\left\{\begin{matrix}b=\frac{m-9p+1}{3p}\text{, }&p\neq 0\\b\in \mathrm{R}\text{, }&m=-1\text{ and }p=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3p by b+3.

$$3pb+9p=m+1$$

Subtract 9p from both sides.

$$3pb=m+1-9p$$

The equation is in standard form.

$$3pb=m-9p+1$$

Divide both sides by 3p.

$$\frac{3pb}{3p}=\frac{m-9p+1}{3p}$$

Dividing by 3p undoes the multiplication by 3p.

$$b=\frac{m-9p+1}{3p}$$

Solve for m

$$m=3p\left(b+3\right)-1$$

Solution Steps

Use the distributive property to multiply 3p by b+3.

$$3pb+9p=m+1$$

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

$$m+1=3pb+9p$$

Subtract 1 from both sides.

$$m=3pb+9p-1$$