Question

What number line represents the solution set for the inequality 3x < –9?

Answer 1

3x < - 9
x < -9/3
x < -3

The number line will have a clear circle at -3 and will be shaded to the left of the number.

Answer 2

x<-3 i.e. the region in the number line to the left of -3 excluding -3

Explanation:

given that inequality as 3x<-9

Since 3 is positive, we can divide this inequality by 3 without disturbing the less than sign

i.e. x<-9/3

Or x<-3

Since strictly less than is there for -3, we must have a hole at -3 (excluding -3)

Since less than sign is there, the region on the number line to the left of -3 with a hole at -3

Hence draw a number line with 0 at centre, mark -3 to left of 0 and circle it.

Shade the region to the left of the smaller circle around -3