Question

Buenas, alguien me ayuda? Inecuaciones de valor absoluto

Answer 1

Respuesta:

8) x e < -∞, -2 ]

7) x e  [ -32/7 , 4/7 ]

Explicación paso a paso:

8-. | x-7| ≥ | x+11 |

x-7 - (x+11) ≥ 0 ; x-7 ≥ 0 ; x+11 ≥ 0

-(x-7)-(x+11) ≥ 0 ; x-7 < 0 ;  x+11 ≥ 0

x-7-(-(x+11)) ≥ 0 ; x-7 ≥0 ; x+11<0

-(x-7)-(-(x+11)) ≥ 0 ; x-7<0 ; x+11 < 0

x e Ф

x  e [ -11 , -2]

x e Ф

x e < -∞ , -2 ]

----

x e < -∞, -2 ]

__________________________

7-. $|\frac{7x}{10} +\frac{7}{5}|\leq \frac{9}{5}$

separa la desigualdad en 2 posibles casos.

$\frac{7x}{10}+\frac{7}{5} \leq \frac{9}{5} ; \frac{7x}{10}+\frac{7}{5} \geq 0\\-(\frac{7x}{10}+\frac{7}{5} ) \leq \frac{9}{5} ; \frac{7x}{10}+\frac{7}{5} \leq 0\\\frac{7x}{10}+\frac{7}{5} \leq \frac{9}{5} ; \frac{7x}{10}+\frac{7}{5} \geq 0\\- ( \frac{7x}{10}+\frac{7}{5} ) \leq \frac{9}{5} ; \frac{7x}{10}+\frac{7}{5} \leq 0\\x\leq 4/7 ; x\geq -2 ; x\geq -32/ 7 ; x < -2\\entonces: \\x e [ -32/7 ; 4/7 ]$