Question #70e44

1 Answer
Apr 16, 2017

Answer:

#x in {+5, +2}#

Explanation:

Case #1#: the absolute value is positive

#3m = m^2 - 10#

#0 = m^2 - 3m - 10#

#0 = (m - 5)(m + 2)#

#m = 5 or -2#

Case #2#: the absolute value is negative

#3m = -(m^2 - 10)#

#3m = -m^2 +10#

#m^2 + 3m - 10 = 0#

#(m + 5)(m - 2) = 0#

#m = -5 or 2#

However, the negative solutions are extraneous because the left hand side would be negative while the right hand side would be positive (by the definition of #|a|#).

Hopefully this helps!