If `4x - 12 ge x + 9`, which of the following must be true ?

Options

A. `x gt 6`
B. `x lt 7`
C. `x ge 7`
D. `x gt 8`

Answer

To solve the inequality \(4x - 12 \geq x + 9\), we will follow these steps:

### Step 1: Rearrange the inequality
Start with the original inequality:
\[ 4x - 12 \geq x + 9 \]

### Step 2: Move all terms involving \(x\) to one side
Subtract \(x\) from both sides:
\[ 4x - x - 12 \geq 9 \]
This simplifies to:
\[ 3x - 12 \geq 9 \]

### Step 3: Move the constant term to the other side
Add 12 to both sides:
\[ 3x \geq 9 + 12 \]
This simplifies to:
\[ 3x \geq 21 \]

### Step 4: Solve for \(x\)
Divide both sides by 3:
\[ x \geq \frac{21}{3} \]
This simplifies to:
\[ x \geq 7 \]

### Conclusion
The solution to the inequality is:
\[ x \geq 7 \]
Thus, the statement that must be true is that \(x\) is greater than or equal to 7.

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