Question

What is the interval notation for the compound inequality? x ≤ −4 or x ≥ 5

Answer 1

Answer:

(-∞, -4] ∪ [5, ∞)

Step-by-step explanation:

Hi!

Alright, so greater (or less) than or equal to is denoted with a bracket.

If x is less than or equal to -4, then the bracket is on the left side.

(___, -4]

Because x is any number under or equal to -4, x can range from negative infinity. However, we use a parentheses for infinity because infinity can never truly be reached.

So, x $\leq$ -4 = (-∞, -4]

X$\geq$5

Equal to = bracket

X is any number above 5, so

[5, ∞)

Because we want both of these, we use the union sign (∪)

so,

= (-∞, -4] ∪ [5, ∞)