Question

Make a number line and mark all the points that represent the following values of x<=-2 or x<-5

Answer 1

Recall that:

1) The solution set of the inequality:

`x\leq b`

is the following interval:

`(-\infty,b\rbrack.`

2) The solution set of the inequality:

`xis the following interval:[tex](-\infty,b).`

Therefore the solution set of the given inequalities is:

`(-\infty,-2\rbrack\cup(-\infty,-5).`

Since -5<-2 then:

`(-\infty,-5)\subseteq(-\infty,-2\rbrack,`

Therefore:

`(-\infty,-2\rbrack\cup(-\infty,-5)=(-\infty,-2\rbrack.`

The representation of the above interval in a number line is:

Answer: