Question

Which value of x is in the solution set of the following inequality -x+8 greater than 6

Answer 1

All real numbers less than
`2`

Explanation:

we have

`-x+8 > 6`

solve for x

Multiply by
`-1` both sides

`x-8 < -6`

Adds
`8` both sides

`x < -6+8`

`x < 2`

The solution is the interval-------->
`(-infinite,2)`

All real numbers less than
`2`

In a number line, the solution is the shaded area to the left of the dashed line at
`x=2` (open circle)

see the attached figure

Answer 2

`- x + 8 > 6`
subtract 8 on both sides


`- x > - 2`
then divide -x on both sides
then you get


`x < 2`
when you divide or multiply by a negative the sign would flip in this case it went from greater than to less than.