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?

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

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, ∞)