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How do you solve #abs(k-10)=3#?

Answer 1

Hazel Anglin

#k = 7, k = 13#

#|k-10| = 3# is really two problems:

#+(k-10) = 3# and #-(k-10) = 3#

Solve each one: #k - 10 = 3# #k -10 + 10 = 10 + 3# #k = 13#

#-(k-10) = 3# #-k+10 = 3# #-k+10-10 = 3-10# #-k = -7# #k = 7#

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Answer 2

Nathan Axel

To solve the equation abs(k - 10) = 3, you would first isolate the absolute value expression by considering two cases:

When k - 10 is positive or zero: In this case, abs(k - 10) = k - 10, so you would have k - 10 = 3. Solve for k: k = 3 + 10 = 13.
When k - 10 is negative: In this case, abs(k - 10) = -(k - 10), so you would have -(k - 10) = 3. Solve for k: -k + 10 = 3 -k = 3 - 10 -k = -7 k = 7.

So, the solutions to the equation abs(k - 10) = 3 are k = 13 and k = 7.

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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.