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Inecuaciones - matematicas
1.
EL ROSARIO NARIÑO INSTITUCION
EDUCATIVA NUESTRA SEÑORA DEL ROSARIO (N) MATEMATICAS INECUACIONES PRESENTADO A: ING: Diego Solarte PRESENTADO POR: Ana Yulissa Córdoba Pérez Ángela Daniela López Angulo
2.
1. 3x +
9 >5 3x > 5-9 3x > -4 x > -4/3 x > -1,33 2. 3x + 6 < 5 3x < 5 – 6 3x < -1 x < - 1/ 3 x < - 0,33 -2 - 1 0 1 2 -2 - 1 0 1 2 S = (-1,33 + ∞) S = (- ∞ , -0.33) -1,33 -0,33 INECUACIONES
3.
3. 9 >
7 – 8 X 8 X > 7 – 9 8 X > - 2 X > - 1/4 X > - 0,25 4. 1/5 X + 9/4 ≥ 8 1/5 X ≥ 8 - 9/4 1/5 X ≥ 1,75 X ≥ 8,75 (-0,25, + ∞) S = [ 8,75, + ∞) -2 - 1 0 1 2 -0,25 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 8,75
4.
5. -8/5 X
- 14 ≤ - 2 - 14 + 2 ≤ 8/ 5 X - 12 ≤ 8/5 X - 60 ≤ 8 X - 60/8 ≤ X - 30/8 ≤ X - 15/2 ≤ X - 7,5 ≤ X 6. - 2 X + 4 ≤ 3 X + 8 -2 X - 3 X ≤ 8 – 4 - 5 X ≤ 4 X ≤ 4/5 X ≤ -0,8 (- ∞, -0,8 ] (- ∞, - 7,5 ] -2 - 1 0 1 2 -0,8 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 -7,5
5.
7. 𝑋2 - X
- 6 < 0 ( X – 3 ) ( X + 2 ) < 0 CASO 1 + - < - CASO 2 - + < - CASO 1 ( X - 3 ) > 0 ˄ X + 2 < 0 X > 3 ˄ X < - 2 CASO 2 ( X – 3 ) < 0 ˄ ( X + 2 ) > 0 X < 3 ˄ X > - 2 ( X – 3 ) ( X + 2 ) < 0 ( X – 3 ) ( X + 2 ) < 0 S = ( - 2 , 3 ) S = Ø 0 3 ˄ -2 0 0 3 -2 0 -2 0 3 S = ( - 3 , 2 ) - -3 + 0 + + - - - - + + + -3 - 0 - 2 +
6.
8. X2 - 5
X 24 ≤ 0 ( X – 8 ) ( X + 3 ) ≤ 0 ( X – 8 ) ( X + 3 ) X2 - 5 X – 24 ≤ 0 S = [- 8 , 3 ] S= (- ∞ , 8 ) 0 ( 3 + ∞ ) __ __ + + + + __ __ __ __ 0 + + 3 + + __ 0 __ + + -8 0
7.
9. 18 X
– 3 X2 > 0 X ( 18 – 3 X ) > 0 18 – 3 X > 0 18 > 3 X 18/3 > X 6 > X = X < 6 X X < 6 18 X – 3 X2 > 0 S= (- ∞ , 0 ) ( 6 + ∞ ) __ __ __ + + + __ __ __ 0 __ __ 6 + + + 0 ___ __ + 0
8.
10. 6 X2 -
7 X – 3 > 0 X1,2 = −𝑏± 𝑏2−4𝑎𝑐 2𝑎 a X2 + b x + c = ( x + j ) ( x + j ) a= 6 b= -7 C= -3 X 1 , 2 = 7± 49−4(6𝑋 −3) 12 X 1, 2 = 7± 121 12 X 1,2 = 7±11 12 X 1 = 7+11 12 = 1,5 X 2 = 7−11 12 = -0,33 6X2 - 7X - 3 > 0 ( X - 1, 5 ) ( X + 0 , 33 ) > 0 CASO 1 X – 1 , 5 > 0 ˄ X + 0,33 > 0 X > 1,5 ˄ X > - 0,33 S1 = (1,5 + ∞ ) S2 = (0,33 + ∞ ) 0,33 1,5 -0,33 SF = ( 1,5 + ∞ ) CASO 2 X – 1 , 5 < 0 ˄ X + 0 , 3 < 0 X < 1 ,5 ˄ X < - 0,33 0 1,5 -0,33 0 SF = ( - ∞ , 0,33 ) ˄
9.
• 6 X2 -
7 X - 3 > 0 ( X + 1 ,5 ) ( X – 0,33 ) > 0 ( X 1,5 ) ( X – 0,33) ( 6 X2 - 7 X – 3 > 0 ) S= (- ∞ , 0,33 ) 0 ( 1,5 , + ∞ ) __ __ __ __ __ + + + __ __ + + + + + + __ __ + + 0 1,5 -0,33 0 -0,33 0 1,5
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