Question

part 3 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≥3
graph the inequality x≤ - 4. choose the correct graph below.
graph the inequality x≥3. choose the correct graph below.
graph the solution set on the number line. choose the correct graph below.

Explanation:

Step1: Analyze \(x\leq - 4\)

The inequality \(x\leq - 4\) includes all real - numbers less than or equal to \(-4\). On a number line, we use a closed circle at \(-4\) (because \(x\) can equal \(-4\)) and draw an arrow to the left.

Step2: Analyze \(x\geq3\)

The inequality \(x\geq3\) includes all real - numbers greater than or equal to \(3\). On a number line, we use a closed circle at \(3\) (because \(x\) can equal \(3\)) and draw an arrow to the right.

Step3: Analyze the compound “or” inequality

For \(x\leq - 4\) or \(x\geq3\), the solution set is the union of the two sets. We combine the two number - line graphs.

Answer:

For \(x\leq - 4\): The correct graph has a closed circle at \(-4\) and an arrow to the left.
For \(x\geq3\): The correct graph has a closed circle at \(3\) and an arrow to the right.
For the solution set of \(x\leq - 4\) or \(x\geq3\): The correct graph has a closed circle at \(-4\) with an arrow to the left and a closed circle at \(3\) with an arrow to the right.