Solve the equation $\left|y+2\right|=4$. Also 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 $\left|y+2\right|=4$, y is the variable which is the unknown quantity.

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 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.

Given $\left|y+2\right|=4$.

Here, $y+2$can be both positive as well as negative.

Case 1. $y+2=4$.

Now solve, $y+2=4$.

Add $-2$in both sides of the equation.

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

Case 2. $y+2=-4$.

Now solve, $y+2=-4$.

Add $-2$in both sides of the equation.

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

Hence, from case $1$ and case $2$, the values of y are $2$ and $-6$respectively.

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