Question

hw sec. 2.6
score: 0.5/8 0/8 answered
question 1
solve for ( x ): ( |x| - 3 = 5 )
( x = )
enter your answer as a list of integer or decimal numbers separated with com
enter dne for does not exist, ( infty ) for infinity

Explanation:

Step1: Isolate the absolute value term

To solve \(|x| - 3 = 5\), we first add 3 to both sides of the equation to isolate the absolute value term.
\[
|x| - 3 + 3 = 5 + 3
\]
\[
|x| = 8
\]

Step2: Solve for \(x\) using the definition of absolute value

The absolute value of a number \(x\), denoted \(|x|\), is the distance from \(x\) to 0 on the number line. So, if \(|x| = 8\), then \(x\) can be either 8 or -8 because both 8 and -8 are 8 units away from 0.
So we have two cases:

• Case 1: \(x = 8\) (since \(|8| = 8\))
• Case 2: \(x = - 8\) (since \(|-8| = 8\))

Answer:

8, -8