Question

Find the set of values of x for which x^2-x-6>0 and 10-2x<5

Answer 1

No Solution.

Explanation:

For starters, here are our two equations:

`(x^2-x-6)>0`

`10-2x<5`

The first option is to solve for x in our second equation. First, we add 2x to both sides to get
`10<5+2x`. Then, we subtract 5 from both sides to get
`2x<5`. Finally, we divide both sides by 2 to get
`x<2.5`. We can plug in 2.5 into our second equation to test if it works. If it does not work, then anything less than 2.5 won't work, and the solution would be impossible.

Now we can plug in our values into our first equation. We now have the equation
`2.5^2-2.5-6>0`. We can simplify to get
`-2.25>0`. This test failed, so there are no solutions. A solution would be impossible.