Question

Which number line represents the solution set for the given inequality?
x+1 ≤-3 or-4x<-8

Answer 1

x ≤-4 or x> 2

Explanation:

x+1 ≤-3 or-4x<-8

First solve the inequality on the left

x+1 ≤-3

Subtract 1 from each side

x+1-1 ≤-3-1

x ≤-4

Then solve the inequality on the right

-4x<-8

Divide each side by -4, remembering to flip the inequality

-4x/4 > -8/-4

x > 2

Put them back together

x ≤-4 or x> 2

Closed circle at -4 and line going to the left and open circle at 2 and line going to the right