Question

Solve the compound inequality: 5z+3<-7 or -2z-6>-8

Answer 1

z<-2 or z<1

Explanation:

The compound inequality to be solved is

5z+3<-7 or -2z-6>-8

`\implies \:5z<-7 - 3 \: or -2z>-8 + 6`

`\implies \:5z<-10 \: or -2z>-2`

`\implies \: (5z)/(5) < ( - 10)/(5) \: or (-2z)/(-2) > ( - 2)/( - 2)`

Simplifying we get,

z<-2 or z<1

NB: the inequality sign at the right side of or has changed because we have divided through by -2