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How do you solve #abs(x-3)> 5#?

Answer 1

Eva Abramson

x > 8 or x < -2

I x-3 I must be zero or positive

Consider I x - 3 I = 5

In this case x = 8 or x = -2

Now think about numbers either side of 8 and -2

If necessary substitute 7, 9 and -3 ,-1 into the original expression to see which side of 8 and -2 you need to be.

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Answer 2

Eli Assouline

Solve |x - 3| > 5

Separate solving in 2 cases:

a. x - 3 > 5 --># x > 8#

b. -(x - 3) = -x + 3 > 5 -> x < 3 - 5 --># x < -2#

Graph:

==========|-2------|0-----------------|8=============

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Answer 3

Eli Assouline

To solve the inequality |x - 3| > 5, follow these steps:

Split the absolute value inequality into two separate inequalities: x - 3 > 5 and x - 3 < -5.
Solve each inequality separately:
- For x - 3 > 5: Add 3 to both sides to isolate x. Then, x > 8.
- For x - 3 < -5: Add 3 to both sides to isolate x. Then, x < -2.
Combine the solutions: -2 < x < 8.

Therefore, the solution to the inequality |x - 3| > 5 is -2 < x < 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 #abs(x-3)&gt; 5#?

How do you solve #abs(x-3)> 5#?