(x+1)(x-2) > 4
x^2 - x - 2 > 4
x^2 - x - 6 > 0
(x-3)(x+2) > 0

So either x-3 and x+2 are both positive, which will be true when x > 3, or both x-3 and x+2 are negative, which will be true when x < -2.

Hi All,

We're asked for the range of values of X that satisfy the inequality (X+1)(X-2) > 4. This question can be approached in a couple of different ways, including by TESTing VALUES.

IF... X=10, then (11)(8) = 88 which is greater than 4. Thus, X=10 is a possible solution.
Eliminate Answers B and D.

IF... X= - 10, then (-9)(-12) = 108 which is also greater than 4. Thus, X = -10 is also a possible solution.
Eliminate Answers A and C.
..
There's only one answer remaining.

Final Answer: E

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Find the range of values of \(x\) that satisfy the inequality \((x+1)(x-2)>4\).

A. \(x > -2\)
B. \(x < -2\)
C. \(x > 3\)
D. \(x < 3\)
E. \(x > 3\) or \(x < -2\)

OA E

(x + 1)(x - 2) > 4

x^2 - x - 2 > 4

x^2 - x - 6 > 0

(x - 3)(x + 2) > 0

To have (x - 3)(x + 2) > 0, EITHER x - 3 > 0 and x + 2 > 0 OR x - 3 < 0 and x + 2 < 0. In the former case, we have x > 3 and x > - 2, which really means x > 3. In the latter case, we have x < 3 and x < -2, which really means x < -2. So the correct answer is x > 3 or x < -2.

Answer: E