In Exercises 61–76, solve each absolute value equation or indicat...

Question

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution.

|x + 1| + 5 = 3

Accepted Answer

Hello today we're going to solve the following absolute value equation. So the equation given to us is the absolute value of X plus plus 27 is equal to one. Now in order to solve for this, I need to go ahead and isolate this absolute value quantity and in order to do that I can go ahead and subtract 27 to both sides of this equation. Doing so is going to give me the absolute value of X plus is equal to negative 26. Now there's an issue with this statement and the issue is is that the saying that the absolute value is equal to a negative number. Now remember that the absolute value allows you to represent any number as a positive number and that means that the number is always going to be greater than or equal to zero. But the issue with this statement is that it's saying the absolute value is equal to a negative number which is less than zero. So this statement is not a true statement, meaning that there is no solution to this equation. And since there's no solution to this equation, the answer to this problem is going to be d. So I hope this video helps in understanding how to solve this type of problem. And I'll go ahead and see you all in the next video

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