Which of the following numbers is NOT a solution of the inequality `3x-5 ge 4x-3`?

Options

A. `-1`
B. `-2`
C. `-3`
D. `-5`

Answer

To solve the inequality \(3x - 5 \geq 4x - 3\) and determine which number is NOT a solution, we will follow these steps:

### Step 1: Rewrite the inequality
Start with the given inequality:
\[ 3x - 5 \geq 4x - 3 \]

### Step 2: Move all terms involving \(x\) to one side
Subtract \(3x\) from both sides:
\[ -5 \geq 4x - 3 - 3x \]
This simplifies to:
\[ -5 \geq x - 3 \]

### Step 3: Isolate \(x\)
Add \(3\) to both sides:
\[ -5 + 3 \geq x \]
This simplifies to:
\[ -2 \geq x \]
or equivalently,
\[ x \leq -2 \]

### Step 4: Determine the solution set
The solution to the inequality is \(x \leq -2\). This means any number less than or equal to \(-2\) satisfies the inequality.

### Step 5: Identify the number that is NOT a solution
Now, we need to check which of the given options is NOT a solution. Since we know that any number greater than \(-2\) is not a solution, we can check the options provided.

Assuming the options include numbers like \(-3, -2, -1, 0\):
- \(-3\) is a solution (since \(-3 \leq -2\))
- \(-2\) is a solution (since \(-2 \leq -2\))
- \(-1\) is NOT a solution (since \(-1 > -2\))
- \(0\) is NOT a solution (since \(0 > -2\))

Thus, the numbers that are NOT solutions are \(-1\) and \(0\). If we need to choose one, \(-1\) is a clear choice.

### Final Answer:
The number that is NOT a solution of the inequality \(3x - 5 \geq 4x - 3\) is \(-1\).

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