Question

1046. 1) |x|>10; 2) |x|<8,14; 3) |x|<3 5/6; 4) |x|>20.​

Answer 1

Ответ:

Пошаговое объяснение:

1) |x| > 10 ⇒  x > 10; x < -10;   ⇒ x ∈ (-∞; -10) ∪ (10; +∞)

2)  |x| <  8,14 ⇒  x < 8,14; x >  -8,14;  ⇒ x∈ (-8,14; 8,14)

3)

$\displaystyle |x| - 3\frac{5}{6} \Rightarrow x \in \bigg ( - 3\frac{5}{6} ; 3\frac{5}{6} \bigg )$

4) |x|>20; ⇒  x > 20; x < -20;   ⇒ x ∈ (-∞; -20) ∪ (20; +∞)

Answer 2

Let's analyze each of these inequalities:

1. |x| > 10: This inequality means that the absolute value of x is greater than 10. In other words, x is either greater than 10 or less than -10:

x > 10 or x < -10

2. |x| < 8.14: This inequality means that the absolute value of x is less than 8.14. In other words, x must be between -8.14 and 8.14:

-8.14 < x < 8.14

3. |x| < 3 5/6: This inequality means that the absolute value of x is less than 3 5/6, which can be written as an improper fraction as 23/6. In other words, x must be between -23/6 and 23/6:

-23/6 < x < 23/6

4. |x| > 20: This inequality means that the absolute value of x is greater than 20. In other words, x is either greater than 20 or less than -20:

x > 20 or x < -20

So, to summarize:

1. x > 10 or x < -10
2. -8.14 < x < 8.14
3. -23/6 < x < 23/6
4. x > 20 or x < -20