Question

(Y-1/4)-(y-4/5)=(y+4/10)-1

Answer 1

`y=(23)/(60)`

Explanation:

`(y-(1)/(4))-(y-(4)/(5))=(y+(4)/(10) )-1`

• First, let's deal with everything in our parentheses. This includes simplification of fractions and distributing signs.
• Remember than when distributing, everything in the parentheses is affected by whatever is being distributed.

`(y-(1)/(4))-(y-(4)/(5))=(y+(4)/(10) )-1\\(y-(1)/(4))-(y-(4)/(5))=(y+(2)/(5))-1`

• A quick note that we can get rid of the parentheses once there is only addition and subtraction left next to the parentheses.

`(y-(1)/(4))-(y-(4)/(5))=(y+(2)/(5))-1\\y-(1)/(4)-y+(4)/(5)=y+(2)/(5)-1`

• Now that the parentheses are gone, we can add and subtract in any order as long as we don't break the rules of addition and subtraction.

`y-(1)/(4)-y+(4)/(5)=y+(2)/(5)-1\\y-y-(1)/(4)+(4)/(5)=y+(2)/(5)-1\\-2y-(1)/(4)+(4)/(5)=y+(2)/(5)-1`

• Let's move all our fractions to one side, and all our unknowns to the other.

`-2y-(1)/(4)+(4)/(5)=y+(2)/(5)-1\\-3y=(1)/(4)-(4)/(5)+(2)/(5)-1`

• We need a common denominator for our fractions. The quickest way to do this only two different denominators is to multiply the two denominators together.
  `4*5=20`, so we will multiply both the numerator and the denominator by whatever we need to to get
  `20`.

`-3y=(1)/(4)-(4)/(5)+(2)/(5)-1\\-3y=(1)/(4)((5)/(5))-(4)/(5)((4)/(4))+(2)/(5)((4)/(4))-1\\-3y=(5)/(20)-(16)/(20)+(8)/(20)-1`

• add the denominators together.
  `-1=-(20)/(20)`

`-3y=(5)/(20)-(16)/(20)+(8)/(20)-1\\-3y=(5)/(20)-(16)/(20)+(8)/(20)-(20)/(20)\\-3y=(13)/(20)-(36)/(20)\\-3y=(-23)/(20)\\-(1)/(3)(-3y)=-(1)/(3)(-(23)/(20))\\y=(23)/(60)`

Answer 2

Explanation: