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": ["$x \\geq -1$", "$x < -4$"]}

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