Question

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

Answer 1

`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`

Answer 2

`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"`