Luca shows his work in finding the solution to 2 − 6x = 5 − 5(x − 1). After checking his answer in the original equation, he found that it did not work. Where did he make a mistake? Step 1: He distributed incorrectly. Step 2: He added 5x incorrectly. Step 3: He simplified incorrectly. Step 4: He subtracted 2 incorrectly.

Luca likely made a mistake in Step 1: He distributed incorrectly.

When distributing on the right side of the equation, the correct distribution of -5 over (x – 1) should give you -5x + 5 (not just -5x). This could lead to errors in further simplifications.

To check, let’s evaluate the equation step-by-step:

1. Start with the original equation:

( 2 – 6x = 5 – 5(x – 1) )

2. Distribute on the right:

( 2 – 6x = 5 – 5x + 5 )

So, it simplifies to:

( 2 – 6x = 10 – 5x )

3. Now, you can move to collect like terms, which might have led to the mistake.

By ensuring the distribution is done correctly, it’s easier to avoid incorrect solutions. If you have more questions or want to clarify further, feel free to ask or check the extended services page!