Solve equation $\left|3z-3\right|=9$and then graph the solution set.

Variables: - In any expression or equation, the variable is an unknown quantity. It may be any alphabet or any special symbol.

In $\left|3z-3\right|=9$, z is a variable.

Constants: - In any expression or equation, the constants are the values that are fixed.

While performing addition in an equation, the same kind of elements or like terms are added together.

Absolute value: - Absolute value of any quantity simply means the positive value of that quantity.

Example: -

Consider a variable x. Here, x can be both positive or negative but $\left|x\right|$will always be positive and hence the absolute value.

Given $\left|3z-3\right|=9$

Case 1: -$3z-3=9$

Add 3 to both sides of the equation.

$\begin{array}{l}3z-3+3=9+3\\ 3z-0=12\\ 3z=12\end{array}$

Multiply both sides by $\frac{1}{3}$.

$\begin{array}{l}\frac{1}{3}\times 3z=\frac{1}{3}\times 12\\ z=4\end{array}$

Case 2: -$3z-3=-9$

Add 3 to both sides of the equation.

$\begin{array}{l}3z-3+3=-9+3\\ 3z-0=-6\\ 3z=-6\end{array}$

Multiply both sides by $\frac{1}{3}$.

$\begin{array}{l}\frac{1}{3}\times 3z=\frac{1}{3}\times \left(-6\right)\\ z=-2\end{array}$

Hence the value of n are $z=-2$and $z=4$.

Consider a number line as z. Mark the points $z=-2$and $z=4$on that number line as shown below: