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How do you solve #abs( 4 - 2/7x )+ 2 = 14#?

Answer 1

Nathan Axel

#color(green)( x = -28 or x = 56#

#abs( 4 - 2/7x )+ 2 = 14#

Transposing #2# to the other side, we get:

#abs( 4 - 2/7x ) = 14 - 2#

#abs( 4 - 2/7x ) = 12#

This implies that :

#4 - 2/7x = 12 or 4 - 2/7x = -12 #

#- 2/7x = 12 - 4 or - 2/7x = -12 - 4 #

#- 2/7x = 8 or - 2/7x = -16 #

Multiplying both equations with #-7/2#, we get:

# x = 8*(-7/2) or x = -16*(-7/2) #

#color(green)( x = -28 or x = 56#

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Answer 2

Hazel Anglin

To solve the equation abs(4 - 2/7x) + 2 = 14, follow these steps:

Subtract 2 from both sides of the equation to isolate the absolute value term:

abs(4 - 2/7x) = 12

Remove the absolute value by considering both positive and negative cases:

Case 1: 4 - 2/7x ≥ 0 Solve 4 - 2/7x = 12 Subtract 4 from both sides: -2/7x = 8 Multiply both sides by -7/2 to solve for x: x = -28

Case 2: 4 - 2/7x < 0 Solve -(4 - 2/7x) = 12 Simplify: -4 + 2/7x = 12 Add 4 to both sides: 2/7x = 16 Multiply both sides by 7/2 to solve for x: x = 56

So, the solutions are x = -28 and x = 56.

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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.