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How do you solve and graph the absolute value inequality #abs(2x + 4)> 8#?

Answer 1

Kennedy Adams

Look below for graph #x> 6# , #x> -2#

#|2x + 4| > = +-8#

Let's do #-8# first

#|2x + 4| > -8#

Subtract #4# to both sides

#|2x|# > #-12#

#|x|# > #-6#

Then you absolute value the RH Side

#x > 6#

Now #+8#

Do the same steps

#x > -2#

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Answer 2

Isaiah Anthony

To solve the absolute value inequality |2x + 4| > 8, follow these steps:

Split the absolute value inequality into two separate inequalities:
- 2x + 4 > 8
- 2x + 4 < -8
Solve each inequality separately:
- For 2x + 4 > 8: Subtract 4 from both sides: 2x > 4 Divide both sides by 2: x > 2
- For 2x + 4 < -8: Subtract 4 from both sides: 2x < -12 Divide both sides by 2: x < -6
Combine the solutions: x > 2 or x < -6
Graph the solution set on the number line:
- Draw an open circle at x = 2 and x = -6.
- Shade the area to the right of 2 and to the left of -6, indicating that x > 2 or x < -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.

How do you solve and graph the absolute value inequality #abs(2x + 4)&gt; 8#?

How do you solve and graph the absolute value inequality #abs(2x + 4)> 8#?