Q61. - Algebra 2

Question

Solve each equation. Check the solution.

 

61.  If $\left|\text{x}+1\right|=\text{x}$

Step-by-Step Solution

Answer

There is no solution set for $\text{x}$.

Step 1 - State the definition of absolute value.

The distance of a number from 0 in the number line is called the absolute value and since distance cannot be negative so absolute value is always positive.

Step 2 - Solve the inequality.

If x is a number, then absolute value of x is written as $\left|x\right|$.

 

Here, the inequality is:

 

$\left|x+1\right|=x$

 

Case 1: 

 

 $\begin{array}{c}a=b\\ x+1=x\\ x+1-1=x-1\\ x=x-1\end{array}$

 

Here value of   cannot be determined.

 

Or Case 2:

 

 $\begin{array}{c}a=-b\\ x+1=-x\\ x+1-1=-x-1\\ x+x=-x-1+x\\ 2x=-1\\ x=-0.5\end{array}$

 

The solution is  $-0.5$. Here x has only one value.

Step 3 - Check the solution.

For case 2: $x=-0.5$.

 

Check:

 

$\begin{array}{l}\left|x+1\right|=x\\ \left|-0.5+1\right|=-0.5\\ \left|0.5\right|=-0.5\\ \xcancel{0.5=-0.5}\end{array}$

 

Thus, it is not correct that is $x=-0.5$ is not a solution.

Step 4 - State the conclusion.

Therefore, there is no solution set for  x.