Question

Solve equation $\left|2t-4\right|=8$and then graph the solution set.

Short answer

On solving $\left|2t-4\right|=8$the obtained value is $t=-2$and $t=6$.

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 $\left|2t-4\right|=8$, t is a variable.

Constants: - In any expression or equation, constant are the values which is 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 $\left|2t-4\right|=8$.

Case 1: - $2t-4=8$

Add 4 to both the sides of the equation.

$\begin{array}{l}2t-4+4=8+4\\ 2t+0=12\\ 2t=12\end{array}$

Multiply $\frac{1}{2}$in both the sides of the equation.

$\begin{array}{l}\frac{1}{2}\times 2t=\frac{1}{2}\times 12\\ t=6\end{array}$

Case 2: -$2t-4=-8$

Add 4 to both the sides of the equation.

$\begin{array}{l}2t-4+4=-8+4\\ 2t+0=-4\\ 2t=-4\end{array}$

Multiply $\frac{1}{2}$in both the sides of the equation.

$\begin{array}{l}\frac{1}{2}\times 2t=\frac{1}{2}\times \left(-4\right)\\ t=-2\end{array}$

Hence the values of b are $t=6$and $t=-2$.

Step-4. Graph of the solution set.

Consider a number line as t. Mark the points $t=6$and $t=-2$on that number line as shown below.