Question

graph the compound inequality on a number line.
x ≥ 1 or x > 4
use the tools to enter your answer.
number line with -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 and tools
resources
master it

Explanation:

Step1: Analyze the compound inequality

The compound inequality is \( x \geq 1 \) or \( x > 4 \). We need to graph the union of the solution sets of these two inequalities.

Step2: Graph \( x \geq 1 \)

For \( x \geq 1 \), we use a closed circle at \( x = 1 \) (because the inequality is "greater than or equal to") and shade to the right of \( 1 \).

Step3: Graph \( x > 4 \)

For \( x > 4 \), we use an open circle at \( x = 4 \) (because the inequality is "greater than") and shade to the right of \( 4 \).

Step4: Combine the graphs

Since it's an "or" compound inequality, the solution set is the union of the two solution sets. The graph of \( x \geq 1 \) already includes the region \( x > 4 \) (because all numbers greater than 4 are also greater than or equal to 1). So we just need to graph \( x \geq 1 \) with a closed circle at 1 and shading to the right.

Answer:

To graph \( x \geq 1 \) or \( x > 4 \) on the number line:

1. Place a closed circle (filled dot) at \( x = 1 \) (because \( x \geq 1 \) includes 1).
2. Shade the region to the right of \( x = 1 \) (this will also include the region \( x > 4 \) since all numbers greater than 4 are greater than or equal to 1).

(On the given number line tool, use the closed circle at 1 and the shading tool to shade to the right of 1.)