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How do you graph and solve #| x-3 | >8 #?

Answer 1

Ethan Adkins

Solution: #x < -5 or x > 11#. In interval notation: #(-oo, -5) uu(11,oo)#

1) #|x-3| > 8 or x-3 > 8 or x> 11# OR

2) #|x-3| > 8 or x-3 < -8 or x < -5#

Solution : # x < -5 or x > 11# In interval notation: #(-oo, -5) uu(11,oo)#[Ans]

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Answer 2

Avery Alexander

To graph and solve the inequality |x - 3| > 8:

Draw a number line.
Plot the point x = 3.
Identify the intervals where |x - 3| > 8.
Choose a test point from each interval to determine if it satisfies the inequality.
Mark the solutions on the number line.
Shade the regions where the inequality holds true.

To solve algebraically:

Split the inequality into two cases: x - 3 > 8 and x - 3 < -8.
Solve each case separately for x.
Combine the solutions from both cases.

This will give you the solution set for the inequality.

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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 graph and solve #| x-3 | &gt;8 #?

How do you graph and solve #| x-3 | >8 #?