Solve the inequation`2x-3ltx+2le 3x +5, x in R.` Draw the graph of the solution set.

Explanation

We have
`2x-3ltx+2le3x+5rArr2x-3ltx+2 and x+2le3x+5`.
Now, `2x-3ltx+2rArrx-3lt2` [adding -x on both sides]
`rArr x lt 5` [adding 3 both sides]
`rArr x in (-oo,5).`
And `x+2le3x+5rArr3x+5gex+2" "[thereforea leb rArrbgea]`
`rArr2x+5ge2` [adding -x on both sides]
`rArr 2x ge -3` [adding -5 on both sides]
`rArr x ge (-3)/(2)` [dividing both sides by 2]
`rArrx in [(-3)/(2),oo)`.
`therefore` solution set `=(-oo,5)nn[(-3)/(2),oo)=[(-3)/(2),5)`.
We may represent it one the number line, as shown below.