How do you solve #2/3x + 4 = 3/5x - 2#?

1 Answer
Mar 10, 2018

Answer:

#x = -90#

Explanation:

Given: #2/3x + 4 = 3/5x - 2#

One way to solve this equation is to multiply the whole equation by the common denominator of the two fractions to eliminate fractions:

The least common multiple (LCM) or common denominator of #3 " & "5#:

#" "3: 3, 6, 9, 12, color(red)(15), 18#

#" "5: 5, 10, color(red)(15), 20#

#15/1 xx (2/3x + 4 = 3/5x - 2)#

# 30/3 x + 60 = 45/5x - 30; " " 10x + 60 = 9x - 30#

Move the #x's# to the same side:

#" "10x + 60 = " "9x - 30#
#ul(+" "-9x " " = -9x " ")#
#" "x + 60 = " "-30#
#ul(" " -60 = " "-60#
#" "x = -90#

Check:
#2/3 xx (-90/1) + 4 = 3/5 xx (-90/1) - 2#

#-180/3 + 4 = -270/5 - 2#

#-60+4 = -54 - 2#

#-56 = -56 # QED