Question

2[3|2x-3|-8]-9 ≤5
Va roog

Answer 1

2[3|2x-3|-8]-9 ≤5
2[3|2x-3|-8] ≤5+9
2[3|2x-3|-8] ≤14
3|2x-3|-8≤14:2
3|2x-3|-8≤7
3|2x-3|≤7+8
3|2x-3|≤15
|2x-3|≤15:3
|2x-3|≤5
cazul I: 2x-3≤5
2x≤5+3
x≤8/4
x≤2
x∈(-α, 2]=S1
cazul II:  2x-3≤-5
2x≤-5+3
2x≤-2
x≤-2/2
x≤-1
x∈(-α,-1]=S2
S=S1intersectatS2
S=x∈[-1,2]