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.
Here’s the correct approach to solving the equation:
1. Start with the equation:
(2 – 6x = 5 – 5(x – 1)).
2. Distribute ( -5 ) on the right side:
(2 – 6x = 5 – 5x + 5).
This simplifies to:
(2 – 6x = 10 – 5x).
3. Next, isolate the (x) terms by adding (6x) to both sides:
(2 = 10 + x).
4. Then, subtract (10) from both sides:
(2 – 10 = x)
which simplifies to:
(-8 = x).
Double-checking when you substitute back, both sides should balance. Make sure to carefully distribute and combine like terms in future problems! If you need more help, feel free to ask!