How do you solve #\frac { x } { 2} = \frac { 3+ x } { 5}#?

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Answer 1 · 2016-12-31T08:24:45

Simplify the equation and isolate the variable. See below.

Begin by multiplying both sides of the equation by #5# and then both sides by #2# to get rid of fractions, cancelling where possible.

#x/2*5=(3+x)/cancel5*cancel5#

#=>(5x)/2=3+x#

#=>(5x)/cancel(2)*cancel(2)=(3+x)*2#

#=>5x=2(3+x)#

Use the distributive property to multiply out the right-hand side of the equation, distributing #2# to each term inside the parentheses:

#=>5x=6+2x#

Subtract #2x# from both sides:

#=>5x-2x=6+cancel(2x-2x)#

#=>3x=6#

Divide both sides by #3# to isolate #x#:

#=>(cancel(3)x)/cancel(3)=6/3#

#=>x=2#

Answer 2 · 2016-12-31T11:04:42

#x=2#

#x/2=(3+x)/5#

#x/2=3/5+x/5#

#x/2-x/5=3/5#

#10/1*(5x-2x)/10=3/5*10/1#

#5x-2x=6#

#3x=6#

#x=2#