How do you solve #2.5(6x-4)=10+4(1.5+0.5x)#?

1 Answer
Jim G.
Aug 22, 2017

#x=2#

Explanation:

#"distribute brackets on both sides of the equation"#

#rArr15x-10=10+6+2x#

#"collect terms in x to the left side and numeric values to"#
#"the right side"#

#"subtract 2x from both sides"#

#15x-2x-10=16cancel(+2x)cancel(-2x)#

#rArr13x-10=16#

#"add 10 to both sides"#

#13xcancel(-10)cancel(+10)=16+10#

#rArr13x=26#

#"divide both sides by 13"#

#(cancel(13) x)/cancel(13)=26/13#

#rArrx=2#

#color(blue)"As a check"#

Substitute this value into the equation and if both sides are equal then it is the solution.

#"left side "=2.5(12-4)=2.5xx8=20#

#"right side "=10+4(1.5+1)=10+(4xx2.5)=10+10=20#

#rArrx=2" is the solution"#

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