Question

part 1 of 3
solve the compound inequality. graph the two inequalities on the first two number lines and the solution set on the third number line.
x ≤ - 4 or x ≥ 1
graph the inequality x ≤ - 4. choose the correct graph below.
a. a number - line graph with a closed - circle at - 10 and a closed - circle at - 5 and a line segment between them
b. a number - line graph with a closed - circle at - 5 and an arrow pointing to the right
c. a number - line graph with an open - circle at - 5 and an arrow pointing to the left
d. a number - line graph with an open - circle at - 5 and an arrow pointing to the right

Explanation:

Step1: Analyze inequality $x\leq - 4$

The inequality $x\leq - 4$ includes all real - numbers less than or equal to - 4. On a number line, we represent this with a closed circle at - 4 (because the value - 4 is included in the solution set) and an arrow pointing to the left.

Step2: Check each option

Option A has a closed circle at - 4 and an arrow pointing to the left, which correctly represents $x\leq - 4$. Option B has a closed circle at - 5 and an arrow pointing to the right, which is incorrect. Option C has an open circle at - 4 and an arrow pointing to the left, which represents $x\lt - 4$ (not $x\leq - 4$). Option D has an open circle at - 5 and an arrow pointing to the right, which is incorrect.

Answer:

A.