How do you solve #-\frac { 5} { 4} a + \frac { 1} { 5} a = - \frac { 21} { 50}#?

Get both terms on the left side to have the same denominator, in this case #20# is convenient because it it is the LCM
#((-5*5)/(4*5))a + ((1*4)/(5*4))a=((-21)/(50))#
#((-25)/(20))a + ((4)/(20))a=((-21)/(50))#
#((-21)/(20))a=((-21)/(50))# we can remove #-# signs
when dividing one fraction by another, we can flip the numerator and denominator of the fraction to be divided.
#a=((21)/(50))*((20)/(21))#
#a=((20)/(50))=0.4#
Check the solution By substituting in #a=0.4#. It should result in #-0.42#

#-1.25a + 0.2 a = -21/50#

due to the fact that #-5/4 = -1.25# and #1/5 = 0.2#

#-1.05 a = -21/50#

#a = 21/(50times1.05)#

#a = 0.4 = 2/5#

#"one way is to multiply all terms by the "#
#color(blue)"lowest common multiple of 4, 5 and 50"#

#"the lowest common multiple is 100"#

#cancel(100)^(25)xx-5/cancel(4)^1 a+cancel(100)^(20)/cancel(5)^1 a=cancel(100)^2xx-21/cancel(50)^1#

#rArr-125a+20a=-42larrcolor(blue)"no fractions"#

#rArr-105a=-42#

#"divide both sides by "-105#

#(cancel(-105) a)/cancel(-105)=(-42)/(-105)#

#rArra=42/105=2/5#