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Peyton Velez

Peyton Velez

Answered question

2022-06-20

How do you solve 1 2 x 2 - x > 4 ?

Answer & Explanation

tennispopj8

tennispopj8

Beginner2022-06-21Added 20 answers

Step 1
Bring everything to one side.
1 2 x 2 - x - 4 > 0
Factor that side if possible.
Factor the 1 2 out of all three terms.
1 2 ( x 2 - 2 x - 8 ) > 0
Recognize that
4 × 2 = 8 , and 4 + 2 = 2 .
1 2 ( x - 4 ) ( x + 2 ) > 0
Divide both sides by 1 2
( x - 4 ) ( x + 2 ) > 0
We now have a product of two factors on the left: x - 4 and x + 2 . We are interested in when this product is positive ( > 0 ) .
Both factors depend on x. Therefore, their product will be positive when x is small/large enough to make the factors either both negative or both positive.
The 1st factor, x - 4 is negative when x < 4
The 2nd factor, x + 2 , is negative when x < 2
So both factors will be negative when x < 2
Similarly, both factors will be positive when x > 4
Our solution is all x in both these regions: x < 2 x > 4 .

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