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How do you solve #abs(-2x+4)=6#?

Answer 1

Nathan Axel

There are 2 possibilities #x<2# and #x>2# (we can ignore the possible third possibility #x=2# by inspection).

If #x<2# then #(-2x+4)# is positive and #abs(-2x+4) = (-2x+4)# In which case #-2x+4 = 6# #x=-1#

If #x>2# then #(-2x+4)# is negative and #abs(-2x+4) = 2x-4# in which case #2x-4 = 6# #x=5#

#x=-1# or #x=5#

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Answer 2

Julia Adams

To solve the equation abs(-2x + 4) = 6, you first isolate the absolute value expression, then solve for x.

Split the equation into two cases: -2x + 4 = 6 and -2x + 4 = -6.
Solve each case separately for x. Case 1: -2x + 4 = 6 Case 2: -2x + 4 = -6
Simplify each equation and solve for x. Case 1: -2x = 2 Case 2: -2x = -10
Divide both sides of each equation by -2 to isolate x. Case 1: x = -1 Case 2: x = 5
Verify the solutions by substituting them back into the original equation.

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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.