Question

Solve the inequality 6 > x² - 5x.

Answer 1

Answer:

$-1 < x < 6$

Step-by-step 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

Answer:

Step-by-step 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)