Question

Use the graph to determine the solution of the

inequality |x+1| + 2 > 5.
O (-∞,-4) (2,00)
(-4, 2)
O (0,3)
O
(-∞,0) (3,0)
DONE✔

Answer 1

Answer: Choice A

(-∞,-4) U (2, ∞)

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Work Shown:

|x+1| + 2 > 5

|x+1| > 5 - 2

|x+1| > 3

x+1 > 3 or x+1 < -3

x > 3-1 or x < -3-1

x > 2 or x < -4

x < -4 or x > 2

The portion x < -4 translates to the interval notation of (-∞,-4)

It might be helpful to think of x < -4 as -∞ < x < -4

The x > 2 is the same as 2 < x and the same as 2 < x < ∞. This turns into the interval notation of (2, ∞)

Therefore, we end up with the solution set of (-∞,-4) U (2, ∞)

The U symbol is the union operator to glue together the two intervals.