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
-
Combine Like Terms: Combine the terms with \( x \): \[ 3x + 2x = 5x \] Thus: \[ 5x - 6 = 24 \]
-
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: \[ 5x = 30 \]
-
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
-
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.
-
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.
-
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.