SOLUTION: I am a bit lost, please help me solve... Solve the polynomial inequality and give your answer in interval form. (x − 1)2 ≥ 4 Thank you!!!!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I am a bit lost, please help me solve... Solve the polynomial inequality and give your answer in interval form. (x − 1)2 ≥ 4 Thank you!!!!       Log On


   

Question 995847: I am a bit lost, please help me solve...
Solve the polynomial inequality and give your answer in interval form.
(x − 1)2 ≥ 4
Thank you!!!!
Found 2 solutions by josgarithmetic, addingup:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
(solution removed because was wrong)

You mean maybe, %28x-1%29%5E2%3E=4?

x%5E2-2x%2B1%3E=4
x%5E2-2x%2B1-4%3E=0
x%5E2-2x-3%3E=0
%28x%2B1%29%28x-3%29%3E=0

The critical values of x around which to check are -1, and +3. Viewing the resulting left member as a parabola, it opens upward, and has its vertex BELOW the x-axis. The inequality will be true (having solutions) for x%3C=-1 or x%3E=3.

You can find results numerically by checking any points in the intervals (-infinity,-1], [-1,3], and [3,infinity).

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
(x − 1)2 ≥ 4 Multiply on left
2x-2 ≥ 4 Add 2 on both sides
2x ≥ 6 Divide both sides by 2
x ≥ 3 And now we write it in interval form. We want to say that x is equal or greater than 3:
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[3,∞)
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The bracket on the left means that 3 is INCLUDED, because the problem says that x is equal or greater than. If the problem said that x was greater than, then we would use a parenthesis. So, if it was x > 3 we would write it (3,∞)