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Sonyakkovt
@Sonyakkovt
March 2022
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!срочно! решите неравенство:
а)6-х<2(4-х)
б)5х<4(3+2х)
а)х^2-11х+24<0
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zhenyaM2002
Verified answer
6 - х < 2( 4 - x )
6 - x < 2×4 - 2x
6 - x < 8 - 2x
-x + 2x < 8 - 6
x < 2
x∈ (-∞ ; 2 )
5х < 4(3 + 2x)
5x < 12 + 8x
5x - 8x < 12
-3x < 12 |× (-1) ⇒ меняем знак неравенства
3х > 12
x > 12/3
х > 4
x∈ ( 4 ; + ∞ )
х² - 11х + 24 < 0
вспомогательное уравнение:
х² - 11х + 24 = 0
D = (-11)² - 4*1*24 = 121 - 96 = 25 = 5² ; D>0
x₁ = ( - (-11) - 5)/(2*1) = (11-5)/2 = 6/2 = 3
x₂ = ( - (-11) + 5)/(2*1) = (11+5)/2 = 16/2 = 8
Вычислим знаки на каждом интервале:
+ - +
-------o--------------o-------------
3 8
3<x<8
x∈ (3 ; 8 ) .
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Answers & Comments
Verified answer
6 - х < 2( 4 - x )6 - x < 2×4 - 2x
6 - x < 8 - 2x
-x + 2x < 8 - 6
x < 2
x∈ (-∞ ; 2 )
5х < 4(3 + 2x)
5x < 12 + 8x
5x - 8x < 12
-3x < 12 |× (-1) ⇒ меняем знак неравенства
3х > 12
x > 12/3
х > 4
x∈ ( 4 ; + ∞ )
х² - 11х + 24 < 0
вспомогательное уравнение:
х² - 11х + 24 = 0
D = (-11)² - 4*1*24 = 121 - 96 = 25 = 5² ; D>0
x₁ = ( - (-11) - 5)/(2*1) = (11-5)/2 = 6/2 = 3
x₂ = ( - (-11) + 5)/(2*1) = (11+5)/2 = 16/2 = 8
Вычислим знаки на каждом интервале:
+ - +
-------o--------------o-------------
3 8
3<x<8
x∈ (3 ; 8 ) .