Question

what is the interval notation for the compound inequality? x is less than or equal to -4 or x is greater than or equal to 5?

Answer 1

x is less than or equal to -4 or x is greater than or equal to 5

x <= -4 or x>= 5

There is no intersection of both inequalities when we graph it in number line So, we write the interval notation separately for each inequality

for x<=-4 , x starts at -4  and goes to -infinity because we have less than symbol. Also we have = sign so we use square brackets

Interval notation is (-∞ , -4]

for x>= 5 , x starts at 5  and goes to infinity because we have greater than symbol. Also we have = sign so we use square bracket at 5

Interval notation is [5 , ∞)

Now combine both notation by a 'U' symbol Union

(-∞ , -4] U [5 , ∞)