When solving an absolute value equation, |x + n| = c (where c> 0), either the expression inside the absolute value is equal to c or the opposite of the expression is equal to c. Is this true or false?

Thank you for the opportunity to help you with your question!

-------------------------------------------------------------------------------------------

|x + n| = c , c> 0

implies

x + n =c or -(x + n) = c

So, it is true that expression inside the absolute value is equal to c or the opposite of the expression is equal to c.

For example,

Let n= 2 and c = 5

So,

|x + 2| = 5 implies

x+ 2 = 5 or -(x + 2) = 5

x = 5 - 2 or -x - 2 = 5

x = 3 or -x = 5 + 2

x = 3 or -x = 7

x = 3 or x = -7

So, if x = 3 => |3 + 2| = |5| = 5

If x = -7 => |-7 + 2| = |-5| = 5

ANSWER: TRUE

Secure Information

Content will be erased after question is completed.

Enter the email address associated with your account, and we will email you a link to reset your password.

Forgot your password?

Sign Up