Question

3/x-2<1 dayu 34 balla.

Answer 1

ОДЗ x≠2

все влево и к общему знаменателю

(3-(x-2))/(x-2)<0

(5-x)/(x-2)<0

методом интервалов определяю знаки

-----(2)+++(5)-----

x=0;5/(-2)<0

x=3;2/1>0

x=6;-1/4<0

ответ x=(-∞;2)U(5;+∞)

Answer 2

It looks like you've written an inequality involving fractions and numbers. However, it's a bit unclear due to the formatting. I'm interpreting it as:

$\frac{3}{x-2} < 1$

If this is correct, I can help you solve it. To solve this inequality, you need to isolate $x$ on one side of the inequality sign. Here's how you can do it step by step:

1. Start with the given inequality: $\frac{3}{x-2} < 1$

2. Multiply both sides by $x-2$ to get rid of the fraction. Remember that when you multiply or divide both sides of an inequality by a negative number, you need to reverse the inequality sign. $3 < x - 2$

3. Add 2 to both sides of the inequality to isolate $x$: $3 + 2 < x$ $5 < x$

So, the solution for $x$ is $x > 5$. In interval notation, this can be written as $(5, \infty)$, which represents all values of $x$ greater than 5.

If my interpretation of the inequality was incorrect, please provide more context or clarify the formatting, and I'll be happy to help further!