Question

Solve the equation $\left|y+2\right|=4$. Also graph the solution set.

Short answer

On solving the equation $\left|y+2\right|=4$the obtained values are $y=-6$and $y=2$. Also, the respective graph of the solution set will be: -

Step-by-step solution

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

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.

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

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.

Step-4. Graph of the solution set.

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