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How do you solve and write the following in interval notation: #|x + 8| ≥ 2#?

Answer 1

#x <= -10#
#x >= -6#

#Ix + 8I >= 2# Solve the inequality in 2 parts: a. #(x + 8) >= 2# #x >= 2 - 8 --> #x >= -6# b. -(x + 8) >= 2 #- x - 8 >= 2# #- x > 10# --> #x <= -10# Solution set expressed by intervals: (-inf., -10] and [-6, inf.) Note. The 2 end points are included in the solution set Graph

=========== -10------------ -6=========== 0===============

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Answer 2

Ethan Adkins

To solve the inequality |x + 8| ≥ 2 in interval notation, you would split it into two cases:

x + 8 ≥ 2
x + 8 ≤ -2

For the first case: x + 8 ≥ 2 x ≥ -6

For the second case: x + 8 ≤ -2 x ≤ -10

Combining both cases: [-10, -6]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.