Q4. - Algebra 1

Question

Solve equation $\left|n+7\right|=5$ and then graph the solution set.

Step-by-Step Solution

Answer

On solving $\left|n+7\right|=5$ the obtained value is $n=-2$ and $n=-12$.

The graph of the solution is: -

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 $\left|n+7\right|=5$, n 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 $\left|n+7\right|=5$.

Case 1: - $\left(n+7\right)=5$

Add $-7$ to both sides of the equation.

$\begin{array}{l}n+7-7=5-7\\ n+0=-2\\ n=-2\end{array}$

Case 2: - $\left(n+7\right)=-5$

Add $-7$ to both sides of the equation.

$\begin{array}{l}n+7-7=-5-7\\ n+0=-12\\ n=-12\end{array}$

Hence the value of n are $n=-2$ and $n=-12$.

Step-4. Graph of the solution set.

Consider a number line as n. Mark the points $n=-2$ and $n=-12$ on that number line as shown below.