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How do you solve #|3x + 2| = 14#?

Answer 1

Isaiah Anthony

#x=4,-16/3#

#color(blue)(|\3x+2|=14#

Absolute value

#:.# Absolute value is always positive

Eg.#|6-7|=1#

But #|6-7| # actually equals #1# and #-1#

So,#|\3x+2|=14,-14#

Solve for the first value

#rarr3x+2=14#

#rarr3x=14-2#

#rarr3x=12#

#rArrcolor(green)(x=12/3=4#

Then, solve for the second value

#rarr3x+2=-14#

#rarr3x=-14-2#

#rarr3x=-16#

#rArrcolor(green)(x=-16/3#

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Answer 2

Eli Assouline

To solve the equation |3x + 2| = 14, you need to consider two cases: when 3x + 2 is positive and when it is negative.

Case 1: 3x + 2 is positive: 3x + 2 = 14 Solve for x: 3x = 12, x = 4

Case 2: 3x + 2 is negative: -(3x + 2) = 14 Solve for x: -3x - 2 = 14, -3x = 16, x = -16/3

So, the solutions are x = 4 and x = -16/3.

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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.