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`