Rozwiąż nierówności:
a)
b)
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2+|x-3| > 4
|x-3| > 2
x-3 < -2 lub x-3 > 2
x < 1 lub x > 5
x ∈ (-∞; 1) (5; +∞)
3√2-x > 1+2√2
3√2-1-2√2 > x
x < √2-1
x ∈ (-∞; √2-1)
a) 2 + |x-3| > 4
2 przypadki:
gdy x > 3
x - 3 > 2
x > 5
gdy x < 3
-x + 3 > 2
-x > -1
x < 1
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a)
2+|x-3| > 4
|x-3| > 2
x-3 < -2 lub x-3 > 2
x < 1 lub x > 5
x ∈ (-∞; 1)
(5; +∞)
b)
3√2-x > 1+2√2
3√2-1-2√2 > x
x < √2-1
x ∈ (-∞; √2-1)
a) 2 + |x-3| > 4
|x-3| > 2
2 przypadki:
gdy x > 3
x - 3 > 2
x > 5
gdy x < 3
-x + 3 > 2
-x > -1
x < 1
b)![3\sqrt2 - x > 1 + 2\sqrt2 \\ 1 - \sqrt2 < -x \\ x < \sqrt2 -1 3\sqrt2 - x > 1 + 2\sqrt2 \\ 1 - \sqrt2 < -x \\ x < \sqrt2 -1](https://tex.z-dn.net/?f=3%5Csqrt2+-+x+%3E+1+%2B+2%5Csqrt2+%5C%5C+1+-+%5Csqrt2+%3C+-x+%5C%5C+x+%3C+%5Csqrt2+-1)