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How do you solve #|5x – 2|>= 8#?

Answer 1

Eva Adamson

#x>=2 or x<=-6/5#

# |u(x)| >= a#, in which case we have:

If #u(x) <=-a #, then #u(x) >= a#.

Let's put it to use:

# 5x - 2 <= -8 (eq2)# # 5x - 2 >= 8 (eq1) #2

Equation 1 (# 5x >= 8 + 2#, #rArr 5x >= 10#, #rArr x >= 10/5#, #rArr x >= 2) can be solved.

Equation 2 can be solved as follows: # 5x - 2 <=-8# # rArr 5x \= -8 + 2# #rArr 5x \=-6# #rArr x \= -6/5#

That means that #x>=2 or x<=-6/5#

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Answer 2

Savannah Anderson

To solve the inequality |5x - 2| >= 8, you first isolate the absolute value expression and then solve for x in two separate cases: when the expression inside the absolute value is positive and when it's negative.

Case 1: 5x - 2 >= 8 Case 2: -(5x - 2) >= 8

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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.

How do you solve #|5x – 2|&gt;= 8#?

How do you solve #|5x – 2|>= 8#?