How do you solve #abs(2g-5)=9#?

2 Answers
1s2s2p
May 9, 2018

#g=7or-2#

Explanation:

Due to how #abs()# works, both the positive and negative of the function can be taken, so:
#2g-5=9# or #-(2g-5)=9#, #2g-5=-9#

#2g=14or2g=-4#

#g=7or-2#

Jim G.
May 9, 2018

#g=-2" or "g=7#

Explanation:

#"the expression inside the absolute value bars can be"#
#"positive or negative thus there are 2 possible solutions"#

#2g-5=9larrcolor(magenta)"positive value"#

#"add 5 to both sides and divide by 2"#

#rArr2g=9+5=14rArrg=14/2=7#

#-(2g-5)=9larrcolor(magenta)"negative value"#

#rArr-2g+5=9#

#"subtract 5 from both sides and divide by "-2#

#rArr-2g=9-5=4rArrg=4/(-2)=-2#

#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.

#g=7to|14-5|=|9|=9#

#g=-2to|-4-5|=|-9|=9#

#rArrg=-2" or "g=7" are the solutions"#

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