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Como se resuelve|x + 2| + | - x + 2|>3?

Como se resuelve |x + 2| + | - x + 2|>3.

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Paloma005
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<img src="https://tex.z-dn.net/?f=%20%7Cx%2B2%7C%2B%7C-x%2B2%7C%3E3%5C%5C%20%5C%5C%20%7Cx%2B2%7C%2B%7Cx-2%7C%3E3%5C%5C%20%5C%5C%20%5Cbullet%20%5Ctext%7BPuntos%20cr%5C%27iticos%3A%20%7Dx%2B2%3D0~%5C%26~x-2%3D0%5Cto%20x%3D-2~%5C%26~x%3D2%5C%5C%20%5C%5C%20%5Cbullet%20%5Ctext%7BCuando%20%7Dx%5Cin%28-%5Cinfty%2C-2%29%5C%5C%20%7Cx%2B2%7C%2B%7Cx-2%7C%3E3%5C%5C%20%20-%28x%2B2%29-%28x-2%29%3E3%20%5C%5C%20-2x%3E3%5C%5C%20x%3C-%5Cdfrac%7B3%7D%7B2%7D%5C%5C%20%5C%5C%20%5Cboxed%7BS_1%3D%28-%5Cinfty%2C-2%29%7D%5C%5C%20%5C%5C%20%5Cbullet%5Ctext%7B%20Cuando%20%7Dx%5Cin%5B-2%2C2%29%5C%5C%20%7Cx%2B2%7C%2B%7Cx-2%7C%3E3%5C%5C%20%20%28x%2B2%29-%28x-2%29%3E3%5C%5C%204%3E3%5C%5C%20%5C%5C%20%5Cboxed%7BS_2%3D%5B-2%2C2%29%7D%5C%5C%20%5C%5C%20%5Cbullet%5Ctext%7BCuando%20%7Dx%5Cin%20%5B2%2C%2B%5Cinfty%29%5C%5C%20%7Cx%2B2%7C%2B%7Cx-2%7C%3E3%5C%5C%20%20%28x%2B2%29%2B%28x-2%29%3E3%5C%5C%202x%3E3%5C%5C%20x%3E%5Cdfrac%7B3%7D%7B2%7D%5C%5C%20%5C%5C%20%5Cboxed%7BS_3%3D%5B2%2C%2B%5Cinfty%29%7D%5C%5C%20%5C%5C%20%20" />3 \ \ \ \ |x + 2| + |x - 2|>3 \ \ \ \ \ bullet \ text{Puntos cr \ 'iticos : }x + 2 = 0~ \ &~x - 2 = 0 \ to x = - 2~ \ &~x = 2 \ \ \ \ \ bullet \ text{Cuando }x \ in( - \ infty, - 2) \ \ |x + 2| + |x - 2|>3 \ \ - (x + 2) - (x - 2)>3 \ \ - 2x>3 \ \ x3 \ \ (x + 2) - (x - 2)>3 \ \ 4>3 \ \ \ \ \ boxed{S_2 = [ - 2, 2)} \ \ \ \ \ bullet \ text{Cuando }x \ in [2, + \ infty) \ \ |x + 2| + |x - 2|>3 \ \ (x + 2) + (x - 2)>3 \ \ 2x>3 \ \ x> \ dfrac{3}{2} \ \ \ \ \ boxed{S_3 = [2, + \ infty)} \ \ \ \ " alt = " |x + 2| + | - x + 2|>3 \ \ \ \ |x + 2| + |x - 2|>3 \ \ \ \ \ bullet \ text{Puntos cr \ 'iticos : }x + 2 = 0~ \ &~x - 2 = 0 \ to x = - 2~ \ &~x = 2 \ \ \ \ \ bullet \ text{Cuando }x \ in( - \ infty, - 2) \ \ |x + 2| + |x - 2|>3 \ \ - (x + 2) - (x - 2)>3 \ \ - 2x>3 \ \ x3 \ \ (x + 2) - (x - 2)>3 \ \ 4>3 \ \ \ \ \ boxed{S_2 = [ - 2, 2)} \ \ \ \ \ bullet \ text{Cuando }x \ in [2, + \ infty) \ \ |x + 2| + |x - 2|>3 \ \ (x + 2) + (x - 2)>3 \ \ 2x>3 \ \ x> \ dfrac{3}{2} \ \ \ \ \ boxed{S_3 = [2, + \ infty)} \ \ \ \ " align = "absmiddle" class = "latex - formula"><img src="https://tex.z-dn.net/?f=%20%5Ctext%7BPor%20ende%20%24x%24%20es%20cualquier%20n%5C%27umero%20real%20%7D%20%20" />.