Solve the following inequality. Graph and check your solution.

Question

3 m greater than or equals 12
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Part 1
Solve the inequality.
  
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​(Simplify your answer. Type an​ inequality.)

Answer 1

To solve the inequality \( 3m \geq 12 \), follow these steps:

1. Divide both sides by 3: \[ m \geq \frac{12}{3} \]

2. Simplify the right side: \[ m \geq 4 \]

So the solution to the inequality is: \[ m \geq 4 \]

Graphing the Solution:

You can represent this solution on a number line. The graph will have:

• A solid dot at 4 (indicating that 4 is included in the solution since it is "greater than or equal to").
• An arrow extending to the right from 4, indicating all values greater than 4 are also included.

Checking your Solution:

To verify, you can choose a number greater than 4, such as 5, and check if it satisfies the original inequality:

\[ 3(5) = 15 \quad \text{and} \quad 15 \geq 12 \quad \text{(True)} \]

Now, check a number less than 4, such as 3:

\[ 3(3) = 9 \quad \text{and} \quad 9 \geq 12 \quad \text{(False)} \]

This confirms that our solution \( m \geq 4 \) is correct, as values of \( m \) less than 4 do not satisfy the original inequality.