Question

Solve −x−6≤−3 or −4x+3>−1 and write the solution in interval notation.

Answer 1

[-3,1)

-x-6<_-3 add 6 both sides
-x<_3 divide by negative 1 which means sign switches
x>_-3

-4x+3>-1 subtract 3 both sides
-4x>-4 divide by negative 4 which means sign switches
x<1

1 is the greater bound meaning x can’t be larger than 1

the sign doesn’t include 1 so it’s the parenthesis in interval notation

-3 is the lower bound meaning x can’t be -3 or less than -3 so the interval notation is

The sign includes -3 so it’s brackets in interval notation