How do you solve #x+2/5=-3/2# by clearing the fractions?

Question

Genesis Allen · Accepted Answer

#color(green)(x=-19/10)#
#color(white)("XXX")#see below for solution method by "clearing the fractions"

Given #color(white)("XXX")color(blue)(x+2/5)=color(blue)(-3/2)# We can clear the fractions by multiplying both sides by the #color(red)(LCM)# (Least Common Multiple) of all denominators appearing in the equation. The denominators that we have in the given equation are #color(blue)2# and #color(blue)5#; their color(red)(LCM) is #color(red)(10)#; so we will multiply both sides by #color(red)(10)# #color(white)("XXX")color(red)(10)xx(color(blue)(x+2/5))=color(red)(10)xx(color(blue)(-3/2))# Simplifying #color(white)("XXX")10x+4=-15# #color(white)("XXX")10x=-19# #color(white)("XXX")x=-19/10#

Hazel Anglin · Answer

undefined To solve the equation $ \frac{x + 2}{5} = -\frac{3}{2} $ by clearing the fractions, multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is $ 10 $. This results in $ 2(x + 2) = -15 $. Then solve for $ x $ by distributing and simplifying: $ 2x + 4 = -15 $. Next, isolate $ x $ by subtracting 4 from both sides: $ 2x = -19 $. Finally, divide both sides by 2: $ x = -\frac{19}{2} $. Therefore, the solution to the equation is $ x = -\frac{19}{2} $.