Question

Помогите с неравенствами пожалуйста:
а) | 2x-1 | < 3
б) | 6x+2 | ≥ 5

Answer 1

a) |2x-1|<3
-3<2x-1<3
-2<2x<4
-1<x<2
б) |6x+2|>=5
6x+2>=5
6x>=3
x>=1/2

Answer 2

$1)|2x-1|\ \textless \ 3 \\ 2x-1\ \textless \ 3 \\2x-1\ \textgreater \ -3\\ \\ 2x\ \textless \ 3+1\\ 2x\ \textgreater \ -3+1\\ \\ 2x\ \textless \ 4\\ 2x\ \textgreater \ -2 \\ \\ x\ \textless \ 2 \\ x\ \textgreater \ -1 \\ \\ x\in (-1;2)$

$2)|6x+2| \geq 5 \\ 6x+2 \geq 5\\6x+2 \leq -5 \\ \\ 6x \geq 5-2 \\ 6x \leq -5-2 \\ \\ 6x \geq 3 \\ 6x \leq -7 \\ \\ x \geq 0.5 \\ x \leq -1 \frac{1}{6} \\ \\ x\in (- \infty ;-1 \frac{1}{6} )\cup [0.5;+ \infty )$