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Lógica y Funciones
14 Desigualdades Lineales
MBA. Darwin Gómez Coapaza
DEFINICION
Desigualdades Lineales
DEFINICION
Una desigualdad es una definición que establece que un
número es menor que otro.
DEFINICION
Desigualdades Lineales
REGLAS PARA LAS DESIGUALDADES
Si un número se suma o se resta en ambos lados de una
desigualdad, la desigualdad resultante tendrá el mismo
sentido que la original.
Si a < b, entonces a + c < b + c
Ejemplo
7 < 10, de modo que 7 + 3 < 10 + 3
DEFINICION
Desigualdades Lineales
REGLAS PARA LAS DESIGUALDADES
Si ambos lados de una desigualdad se multiplican o
dividen por el mismo número positivo, la desigualdad
resultante tendrá el mismo sentido que la original.
Si a < b y c > 0, entonces ac < bc
Ejemplo
3 < 7 y 2 > 0, entonces (3)(2) < (7)(2)
DEFINICION
Desigualdades Lineales
REGLAS PARA LAS DESIGUALDADES
Si ambos lados de una desigualdad se multiplican o
dividen por el mismo número negativo, la desigualdad
resultante tendrá el sentido contrario que la original.
Si a < b y c < 0, entonces ac > bc
Ejemplo
4 < 7 y -2 > 0, entonces (4)(-2) > (7)(-2)
DEFINICION
Desigualdades Lineales
REGLAS PARA LAS DESIGUALDADES
Cualquier lado de una desigualdad puede reemplazarse
por una expresión equivalente a ella.
Si a < b y c = 0, entonces c < b
Ejemplo
x < 2, x = y + 4, entonces y + 4 < 2
DEFINICION
Desigualdades Lineales
EJERCICIOS
2 (x – 3) < 4
2x – 6 < 4
2x < 10
x < 5
DEFINICION
Desigualdades Lineales
EJERCICIOS
3 – 2x ≤ 6
– 2x ≤ 3
x ≥ -3/2
DEFINICION
Desigualdades Lineales
EJERCICIOS
3
2
𝑥 − 2 + 1 ≻ −2(𝑥 − 4)
3
2
𝑥 − 2 + 1 ≻ −2 𝑥 − 4
(2)
3 𝑥 − 2 + 2 ≻ −4 𝑥 − 4
3𝑥 − 6 + 2 ≻ −4𝑥 + 16
3𝑥 − 4 ≻ −4𝑥 + 16
7𝑥 ≻ 20
𝑥 ≻ 20/7
DEFINICION
Desigualdades Lineales

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14 desigualdades lineales diapositivas