Questions: Graph the compound inequality on the number line. x ≥ -1 or x < -4

Transcript text: Graph the compound inequality on the number line. \[ x \geq-1 \text { or } x<-4 \]

Solution

Solution Steps

Step 1: Identify the Inequalities

The compound inequality given is: $x \geq -1 \text{ or } x < -4$

Step 2: Solve the Inequalities

The first inequality $x \geq -1$ represents all values of $x$ that are greater than or equal to $-1$ .
The second inequality $x < -4$ represents all values of $x$ that are less than $-4$ .

Step 3: Combine the Solutions

Since the compound inequality uses "or," the solution is the union of the two sets:

$x \geq -1$ includes all numbers from $-1$ to $\infty$ .
$x < -4$ includes all numbers from $-\infty$ to $-4$ .

Final Answer

The solution to the compound inequality is: $x \in (-\infty, -4) \cup [-1, \infty)$

{"axisType": 3, "coordSystem": {"xmin": -6, "xmax": 2, "ymin": -1, "ymax": 1}, "commands": ["x = -1", "x = -4"], "latex_expressions": [" $x \\geq -1$ ", " $x < -4$ "]}