Questions: Solve the following inequality. Graph the solution set and then write it in interval notation. -2 x ≥ 6

Solve the following inequality. Graph the solution set and then write it in interval notation. -2 x ≥ 6
Transcript text: Solve the following inequality. Graph the solution set and then write it in interval notation. \[ -2 x \geq 6 \]
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Solution

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Solution Steps

Step 1: Divide both sides by -2

We have the inequality \(-2x \geq 6\). Divide both sides by \(-2\), remembering to reverse the inequality sign when dividing by a negative number: \(x \leq -3\)

Step 2: Graph the solution

The solution \(x \leq -3\) represents all numbers less than or equal to \(-3\). On a number line, this is represented by a closed circle at \(-3\) (because \(-3\) is included) and an arrow extending to the left towards negative infinity.

Step 3: Write the solution in interval notation

The interval notation for \(x \leq -3\) is \((-\infty, -3]\).

Final Answer

Graph: C Interval notation: \(\boxed{(-\infty, -3]}\)

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