What is the value of #x# in the equation #(3/4)x + 2 = (5/4)x - 6# ?

3 Answers
Apr 17, 2018

#x=16#

Explanation:

#(3/4)x+2=(5/4)x-6#

#2+6=(5/4)x-(3/4)x#

#8=1/2x#

#x=16#

Apr 17, 2018

#x = 16#

Explanation:

Re-arrange the equation.

Add #6# to both sides:

#(3/4)x + 2 + 6 = (5/4)x - 6 + 6#
#(3/4)x + 8 = (5/4)x#

Multiply out #(3/4)x " and " (5/4)x#:

#(3x)/4# and #(5x)/4#

Multiply it all by 4:

#3x + 8(4) = 5x#

Solve:

#3x - 3x + 32 = 5x - 3x#
#32 = 2x#

#x = 16#

Apr 17, 2018

#x=16#

Explanation:

#"collect terms in x on one side of the equation and"#
#"numeric values on the other side"#

#"subtract "3/4x" from both sides"#

#cancel(3/4x)cancel(-3/4x)+2=5/4x-3/4x-6#

#rArr2=1/2x-6#

#"add 6 to both sides"#

#2+6=1/2xcancel(-6)cancel(+6)#

#rArr8=1/2x#

#"multiply both sides by 2"#

#rArrx=16" is the solution"#