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How do you solve #|2a + 10| = | 3a - 8|#?

Answer 1

Avery Alexander

#a=18# or #a=-2/5#

If #|x|=|y|# then either #x=y# or x=-y#

Hence as #|2a+10|=|3a-8|#

either #2a+10=3a-8# i.e. #10+8=3a-2a# i.e #a=18#

or #2a+10=-(3a-8)# i.e. #2a+10=-3a+8#

i.e. #2a+3a=+8-10# i.e. #5a=-2# i.e #a=-2/5#

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Answer 2

Avery Alexander

To solve the equation |2a + 10| = |3a - 8|, we need to consider two cases: when the expressions inside the absolute value signs are positive and when they are negative.

Case 1: When 2a + 10 and 3a - 8 are both positive: 2a + 10 = 3a - 8

Case 2: When 2a + 10 and 3a - 8 are both negative: -(2a + 10) = -(3a - 8)

Solving each case will give us the possible values of a.

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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.