Question

Nine fewer than half a number is five more than four times the number. What is the number?

Answer 1

see a solution process below;

Explanation:

Simply represent the unknown number as `x`

*Nine fewer than half a number;

`1/2x - 9`

*...is five more than four times the number;

`1/2x - 9 = 4 xx x + 5`

What is the number?;

`1/2x - 9 = 4x + 5`

We should solve for the value of `x` to know the number..

`1/2x - 9 = 4x + 5`

`x/2 - 9 = 4x + 5`

Multiply through by `2`

`2(x/2) - 2(9) = 2(4x) + 2(5)`

`cancel2(x/cancel2) - 18 = 8x + 10`

`x - 18 = 8x + 10`

`8x + 10 = x - 18 -> "re-arranging the equation"`

`8x - x = -18 - 10 -> "collecting like terms"`

`7x = -28`

Dividing both sides by `7`

`(7x)/7 = -28/7`

`(cancel7x)/cancel7 = -4`

`x = -4`

Hence, the number is `-4`