Question

The sum of one half and four times a number is equal to five sixths subtracted from five times the number. Find the number.

Answer 1

The sum (addition) of one-half (
`(1)/(2)`) and four (4) times (multiplication) a number (n) is equal to (=) five-sixths (
`(5)/(6)`) subtracted from (subtraction) five (5) times (multiplication) the same number (n).


`(1)/(2)` + 4n = 5n -
`(5)/(6)` Multiply both sides by 6

`(6)/(2)` + 4n = 5n - 5 Simplify the fraction
3 + 4n = 5n - 5 Subtract 5n from both sides
3 - n = -5 Subtract 3 from both sides
-n = -8 Divide both sides by -1
n = 8