Question

Absolute value inequality.

|2w-5|  ((is less than or equal to))  5

Answer 1

`|2w-5| \leq 5\\\\ Formula\ for\ absolute\ value\\\\ |a|=a,\ for\ a \geq 0\\ or\\|a|=-a,\ for\ a<0 \\\\ 1)\\ for\ 2w-5 \geq 0\ \ -->2w \geq 5\ \ -->w \geq 2,5\\ 2w-5 \leq 5\\ 2w \leq 10\ \ |:2\\ w \leq 5\\\\ Product\ of\ w \leq 5\ and\ w \geq 2,5\\ w\in[2,5;5]`
`2)\\for\ 2w-5<0\ \ \ -->2w<5--->\ \ w<2,5\\ -2w+5 \leq 5\\ -2w \leq 0\\ w>0\\\\Product\ of\ w>0\ and\ w<2,5\\\\w\in(0;2,5]\\\\ Summing\ both\ cases\ w\in(0,5]`