Question

Solve equation $\left|b+4\right|=2$and then graph the solution set.

Short answer

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

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 $\left|b+4\right|=2$, b 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 a 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 $\left|b+4\right|=2$.

Case 1: -$b+4=2$

Add $-4$to both sides of the equation.

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

Case 2: - $b+4=-2$

Add $-4$to both sides of the equation.

$\begin{array}{l}b+4-4=-2-4\\ b+0=-6\\ b=-6\end{array}$

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

Step-4. Graph of the solution set.

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