Which of the following is a solution of `(2x -5)/(3) gt (3x + 3)/(4)` ?

Options

A. `x = -5`
B. `x = -2`
C. `x = -29`
D. `x = -30`

Explanation

To solve the inequality \(\frac{2x - 5}{3} > \frac{3x + 3}{4}\), we will follow these steps:

### Step 1: Eliminate the fractions
To eliminate the fractions, we can multiply both sides of the inequality by the least common multiple (LCM) of the denominators, which is 12.

\[ 12 \cdot \frac{2x - 5}{3} > 12 \cdot \frac{3x + 3}{4} \]

### Step 2: Simplify both sides
Now we simplify both sides:

\[ 4(2x - 5) > 3(3x + 3) \]

Distributing on both sides gives:

\[ 8x - 20 > 9x + 9 \]

### Step 3: Rearrange the inequality
Next, we will rearrange the inequality to isolate \(x\). We can subtract \(9x\) from both sides:

\[ 8x - 9x - 20 > 9 \]

This simplifies to:

\[ -x - 20 > 9 \]

### Step 4: Isolate \(x\)
Now, we will add 20 to both sides:

\[ -x > 9 + 20 \]

This simplifies to:

\[ -x > 29 \]

### Step 5: Multiply by -1
To solve for \(x\), we multiply both sides by -1. Remember that when we multiply or divide an inequality by a negative number, we must reverse the inequality sign:

\[ x < -29 \]

### Conclusion
The solution to the inequality is \(x < -29\).

Now, we need to check which of the given options satisfies this inequality. The options are:
- A) -5
- B) -2
- C) -29
- D) -30

Since we need \(x\) to be less than -29, the only option that satisfies this condition is:
- D) -30