Question

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?

Answer 1

Luca made a mistake while simplifying the equation 2−6x=5−5(x−1). His error occurred when combining the constants in the equation.

Step-by-step explanation:

In the equation 2-6x=5-5(x-1), Luca made a mistake while simplifying the equation. Let's go step by step to identify the error:

1. Distribute the -5 to the terms inside the parentheses:
   2-6x=5-5x+5
2. Combine like terms:
   2-6x=10-5x
3. Now, bring the constants to one side of the equation and the variables to the other side:
   2-10=5x-6x
4. Simplify:
   -8=-x
5. We need to isolate x, so multiply both sides of the equation by -1:
   8=x

Luca's mistake is in step 3 when they incorrectly combined the constants. The correct equation should be 2-6x=10-5x. The correct solution is x=8. By substituting x=8 back into the original equation, 2-6(8)=5-5(8-1), we see that both sides of the equation are equal, confirming that x=8 is the correct solution.