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How do you solve # abs(8-2x)=4#?

Answer 1

#x = 2" "# or #" "x = 6#

Since you're dealing with the absolute value of an expression, you know that you're going to have to take into account the fact that the absolute value of a real number returns a positive value regardless of the sign of said number.

This implies that you will have two cases, one in which the expression inside the modulus is positive, and the other when it's negative.

The equation takes the form

#8 - 2x = 4#

#-2x = -4 implies x = ((_4))/((-2)) = 2#

This time, you have

#-(8-2x) = 4#

#-8 + 2x = 4#

#2x = 12 implies x = 12/2 = 6#

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Answer 2

Abigail Allen

To solve the equation abs(8 - 2x) = 4, you can follow these steps:

Set up two equations:
- 8 - 2x = 4
- 8 - 2x = -4
Solve each equation separately for x:
- For 8 - 2x = 4, add 2x to both sides, then subtract 4 from both sides to isolate x.
- For 8 - 2x = -4, add 2x to both sides, then add 4 to both sides to isolate x.
Solve for x in both equations to find the possible solutions.

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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.