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What is the solution set for #abs(2x – 4) = 10#?

Answer 1

#x=-3# or #x=7#

Case 1: #2x-4 >= 0# #abs(2x-4) = 10# #rarr color(white)("XXX") 2x-4 = 10# #rarr color(white)("XXX")2x = 14# #rarr color(white)("XXX")x = 7#

Case 2: #2x-4 < 0# #abs(2x-4) = 10# #rarr color(white)("XXX")4-2x =10# #rarr color(white)("XXX")-2x = 6# #rarr color(white)("XXX")x = -3#

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Answer 2

Hazel Anglin

To find the solution set for ( |2x - 4| = 10 ):

Set up two equations: ( 2x - 4 = 10 ) and ( 2x - 4 = -10 )
Solve each equation separately: For ( 2x - 4 = 10 ): ( 2x = 10 + 4 ) ( 2x = 14 ) ( x = 7 ) For ( 2x - 4 = -10 ): ( 2x = -10 + 4 ) ( 2x = -6 ) ( x = -3 )
Combine the solutions: The solution set is ( { -3, 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.