solve the inequalities below, express the solution on real number line and interval notation

Question

a) (1-x)2 ≥ 4

b) (x-1)² > (2x+1)²

Answer 1

a) (inf, -1]U[3, inf)

x is greater than or equal to 3

or x is less than or equal to -1

b) take square roots

x-1=2x+1

x=-2 is an endpoint between two intervals

but not included

negative square root

1-x =2x+1

x=0 is another not included interval endpoint

(-2,0) is the solution in interval form

or

-2<x<0

use parentheses to show endpoints not included