Question

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

Short answer

On solving $\left|3z-3\right|=9$the obtained value is $z=-2$and $z=4$.

The graph of the solution is: -

Step-by-step solution

Step-1. Apply the concept of Variables and constant.

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.

Step-2. Concept of absolute value.

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.

Step-3. Solution of the given equation.

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 $z=4$.

Step-4. Graph of the solution set.

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