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How do you solve #abs(1/3x - 3) = 9#?

Answer 1

Hazel Anglin

#x=-18" or "x=36#

#"the expression inside the absolute value bars can be"# #"positive or negative leading to 2 possible solutions"#

#1/3x-3=9larrcolor(magenta)"positive value"#

#"add 3 to both sides"#

#rArr1/3x=9+3=12#

#"multiply both sides by 3"#

#rArrx=3xx12=36#

#-(1/3x-3)=9larrcolor(magenta)"negative value"#

#rArr-1/3x+3=9#

#"subtract 3 from both sides"#

#rArr-1/3x=9-3=6#

#"multiply both sides by "-3#

#rArrx=6xx-3=-18#

#color(blue)"As a check"#

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

#x=36to|12-3|=|9|=9#

#x=-18to|-6-3|=|-9|=9#

#rArrx=-18" or "x=36" are the solutions"#

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Answer 2

Eva Abramson

To solve the equation abs(1/3x - 3) = 9, first, split the equation into two separate equations: 1/3x - 3 = 9 and 1/3x - 3 = -9. Then solve each equation individually to find the possible values of x. After solving, the solutions are x = 36 and x = -18.

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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.