Question

Write the solution to the inequality.

m - 9 ≥ -6
m 

 

≥

<

>

≤

 

m=2

m=3 (boundary)

m=4

m - 9 ≥ -6falsetruetrue



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1

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3

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6

Answer 1

To solve the inequality \( m - 9 \geq -6 \), we follow these steps:

1. **Isolate \( m \)**:
\[
m - 9 \geq -6
\]
Add 9 to both sides of the inequality:
\[
m \geq -6 + 9
\]
\[
m \geq 3
\]

2. **Interpret the solution**:
The solution indicates that \( m \) must be greater than or equal to 3.

3. **Final solution**:
The solution can be expressed in interval notation as:
\[
[3, \infty)
\]

This means \( m \) can take any value starting from 3 and going to positive infinity.

For verification:
- If \( m = 3 \): \( 3 - 9 = -6 \) (which satisfies \( \geq -6 \))
- If \( m = 4 \): \( 4 - 9 = -5 \) (which is also greater than -6)
- If \( m = 2 \): \( 2 - 9 = -7 \) (which does not satisfy the inequality)

Therefore, the inequality \( m - 9 \geq -6 \) is true for \( m \geq 3 \).