How do you solve the equation #abs(x-a)=b#?

Answer 1

#x=a+b# or #x=a-b# if #b>=0#.

#|x- a|=b# means that

either #x-a=b# i.e. #x=a+b#

or #x-a=-b# i.e. #x=a-b#

Note that as absolute value of any number is always #0# or positive, hence we should have #b>=0# and if #b<0#, there is no solution.

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Answer 2

Avery Alexander

To solve the equation ( |x - a| = b ), you need to consider two cases:

When ( x - a = b ), solve for ( x ). ( x = a + b )
When ( x - a = -b ), solve for ( x ). ( x = a - b )

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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.

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