Question

1/5 x+ 1/4 = 1/2 (x+5)

Answer 1

`(1)/(5) x+(1)/(4)=(1)/(2)(x+5)\\(1)/(5) x+(1)/(4)=((1)/(2))(x)+((1)/(2))(5)\\(1)/(5) x+(1)/(4)=(1)/(2)x+2(1)/(2) \\(1)/(5) x - (1)/(5) x +(1)/(4) - 2(1)/(2)=(1)/(2)x+2(1)/(2) - 2(1)/(2) - (1)/(5) x\\(1)/(4)-2(1)/(2) = (1)/(2)x-(1)/(5)x\\-2(1)/(4)=(3)/(10)x\\-2(1)/(4)* (10)/(3)=(3)/(10)x * (10)/(3)\\-(15)/(2)= x\\-7.5=x`

Answer:

`x=-7.5`

Check:

`(1)/(5)(-7.5)+(1)/(4)=(1)/(2)[(-7.5)+5] \\-(3)/(2) +(1)/(4)=(1)/(2)(-2.5)\\-(5)/(4) = -(5)/(4)`

Hope this was helpful.