Question

Solve the inequality 6 > x² - 5x.

Answer 1

`-1 < x < 6`

Explanation:

Moving all terms to one side, we get
`x^2-5x-6 < 0`. Notice that we can factor the left side. Doing so, we get
`(x-6)(x+1) < 0`. The zeroes in this equation are
`x-6=0 \Rightarrow x=6` and
`x+1=0\Rightarrow x=-1`. Now, we must create test points in the intervals:
`x < -1, -1 < x < 6, x > 6`. For example, we can choose
`x=-2,x=0,x=7`. For
`x=-2`, we get that
`(-2-6)(-2+1) = 8 < 0` is false, since the expression is positive. Doing the same thing for
`x=0` and
`x=7`, we get that only
`x=0` creates a negative value. This means that the values in the interval
`\boxed{-1 < x < 6}` all work.

Answer 2

Explanation:

6 > x² - 5x.

The answer for the inequality is -1 the greater than sign x greater than 6

The interval notation is ( -1,6)