How do you solve #1/9(2m-16)=1/3(2m+4)#?

1 Answer
Jan 29, 2017

Answer:

m = -7

Explanation:

Multiply both sides by 9. This gives us
#9/9 (2m -16) = 9/3(2m + 4)#

which simplifies to

#2m - 16 = 3(2m + 4)#

Simplify the right hand side by multiplying each element by 3
#2m - 16 = 6m + 12#

Add 16 to both sides

#2m - 16 + 16 = 6m + 12 + 16#

which simplifies to

#2m = 6m + 28#

subtract 6m from both sides

#2m - 6m = 6m + 28 - 6m#

which simplifies to

#-4m = 28#

Divide both sides by -4

#((-4)/(-4))m = (28)/(-4)#

which gives us

#m = -7#

Verification
Left hand side

#(1/9)((2 * -7) -16)#
#(1/9)(-14 -16)#
#(1/9)(-30)#
#-30/9#
#-10/3#

Right Hand Side
#(1/3)((2 * -7) + 4))#
#(1/3)(-14 + 4)#
#(1/3(-10))#
#-10/3#

Left side = Right side, proving our answer (m = -7) to be correct.