Question

Read the problem below the problem was solved incorrectly solve the problem correctly then explain the air that was made
3x+2x-6=24
-2x -2x
X-6=24
+6 +6
X=30

Correct work and answer

Explain mistake made

Answer 1

Let's solve the equation step by step and identify the incorrect steps in the original solution.

### Original Problem
The equation given is:
\[ 3x + 2x - 6 = 24 \]

### Correct Steps to Solve
1. **Combine Like Terms**: Combine the terms with \( x \):
\[
3x + 2x = 5x
\]
Thus:
\[
5x - 6 = 24
\]

2. **Add 6 to Both Sides**: To isolate the \( x \) term, add 6 to both sides of the equation:
\[
5x - 6 + 6 = 24 + 6
\]
This simplifies to:
\[
5x = 30
\]

3. **Divide by 5**: Now, divide both sides by 5 to solve for \( x \):
\[
x = \frac{30}{5} = 6
\]

### Final Answer
The correct solution is:
\[
x = 6
\]

### Explanation of the Mistakes Made
1. **Incorrect Combination of Terms**: The first mistake was that the terms \( 3x \) and \( 2x \) were combined incorrectly. The correct combination is \( 3x + 2x = 5x \), but the original solution erroneously subtracts \( 2x \) without combining it properly.

2. **Incorrect Transition Steps**: After miscombining terms, the next transitions made in the provided solution (moving \( -2x \) directly and jumping to \( x - 6 = 24 \)) did not follow the algebraic principles like addition or subtraction properly.

3. **Solving for \( x \)**: The original solution miscalculated the operations leading to an incorrect final value for \( x \) (claiming \( x = 30 \)) instead of the correct \( x = 6 \).

Thus, the correct procedure must include careful step-by-step operations that respect algebraic rules for combining like terms and moving constants across the equal sign.