Question
Solve the inequality \( 3 x \geq-24 \). Write the solution set in interval notation, and graph The solution set is \( \square \). (Simplify your answer. Type your answer in interval notation.)
Ask by Garrett Wilson. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution set is \([-8, \infty)\).
Solution
Solve the equation \( 3x \geq -24 \).
Solve the inequality by following steps:
- step0: Solve for \(x\):
\(3x\geq -24\)
- step1: Divide both sides:
\(\frac{3x}{3}\geq \frac{-24}{3}\)
- step2: Divide the numbers:
\(x\geq -8\)
The solution to the inequality \(3x \geq -24\) is \(x \geq -8\).
The solution set in interval notation is \([-8, \infty)\).
Therefore, the solution set is \([-8, \infty)\).
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Simplify this solution The Deep Dive
To solve the inequality \( 3x \geq -24 \), we start by dividing both sides by 3, yielding \( x \geq -8 \). In interval notation, the solution set is \( [-8, \infty) \). Now, if we were to graph this solution on a number line, we would draw a solid circle at -8 (indicating that -8 is included in the solution) and shade all the numbers to the right of -8, extending towards infinity. This visually represents all numbers greater than or equal to -8. So, the solution set is \( [-8, \infty) \).
