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Solve the inequality 6 > x² - 5x.

2 Answers

0 votes

Answer:


-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.

User Daniel Jackson
by
8.1k points
6 votes

Answer:

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)

User Badazzhindu
by
7.6k points

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