Questions: Solve the compound inequality. Graph the two inequalities on the first two number lines and the solution set on the third number line. x <= -1 or x >= 5 Graph the inequality x <= -1. Choose the correct graph below. A. B. C. D.

Solve the compound inequality. Graph the two inequalities on the first two number lines and the solution set on the third number line.
x <= -1 or x >= 5

Graph the inequality x <= -1. Choose the correct graph below.
A.
B.
C.
D.

Transcript text: Solve the compound inequality. Graph the two inequalities on the first two number lines and the solution set on the third number line. \[ x \leq-1 \text { or } x \geq 5 \] Graph the inequality $\times \leqslant-1$. Choose the correct graph below. A. B. C. D.

Solution

Solution Steps

Step 1: Solve the Compound Inequality

The given compound inequality is $ x \leq -1 $ or $ x \geq 5 $.

Step 2: Graph the First Inequality $ x \leq -1 $

For $ x \leq -1 $, we shade all the numbers to the left of -1, including -1 itself. This is represented by a closed circle at -1 and shading to the left.

Step 3: Graph the Second Inequality $ x \geq 5 $

For $ x \geq 5 $, we shade all the numbers to the right of 5, including 5 itself. This is represented by a closed circle at 5 and shading to the right.

Final Answer

The correct graph for the compound inequality $ x \leq -1 $ or $ x \geq 5 $ is option B. This graph shows a closed circle at -1 with shading to the left and a closed circle at 5 with shading to the right.

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