Question

which set of terms best represents the graphed solution for the inequality |x - 5| + 1 > 5?
option #1: open circles on the end values; two separate solution sets
option #2: open circles on the end values; a single defined solution set
option #3: closed circles on the end values; two separate solution sets
option #4: closed circles on the end values; a single defined solution set
(1 point)
option #

Explanation:

Step1: Solve the inequality \(|x - 5|+1>5\)

Subtract \(1\) from both sides: \(|x - 5|>4\).
By the definition of absolute - value, if \(|a|>b\) (\(b>0\)), then \(a>b\) or \(a < - b\).
So \(x - 5>4\) or \(x - 5 < - 4\).

Step2: Solve \(x - 5>4\)

Add \(5\) to both sides: \(x>4 + 5\), so \(x>9\).

Step3: Solve \(x - 5 < - 4\)

Add \(5\) to both sides: \(x< - 4+5\), so \(x < 1\).

Since the inequality is strict (\(>\)), the endpoints \(x = 1\) and \(x = 9\) are not included in the solution set. The solution set is composed of two separate intervals \(x<1\) and \(x>9\), which are represented by open circles on the end - values.

Answer:

Option #1: open circles on the end values; two separate solution sets