Question

How do you solve `abs(3-2x)= 7`?

Answer 1

`x=-2` or `x=5`

Explanation:

In general
`color(white)("XXX")abs(a)=b`
needs to be treated as two separate possibilities:
`color(white)("XXX")a=+bcolor(white)("XX")orcolor(white)("XX")a=-b`

Therefore, given `abs(3-2x)=7`
we have
#color(white)("XXX"){: (3-2x=+7," or ",3-2x=-7), (-2x=+4," |",-2x=-10), (x=-2," |",x=5) :}#