Kadesha is simplifying the expression below. \( -(x-3)-2(x-1) \) She lists the steps that she uses to simplify the expression as follows: Step 1: Distribute -1 through \( (x-3) \), and distribute -2 through \( (x-1) \). Step 2: Rewrite the expression as \( -x-3-2 x-2 \). Step 3: Combine \( -x \) and \( -2 x \), and combine -3 and -2 . Step 4: The simplified expression is \( -3 x-5 \). She made the first error in Step 1 because only -2 should be distributed through the parentheses. She made the first error in Step 2 because Step 2 should be \( -x+3-2 x+2 \). She made the first error in Step 3 because \( -x \) and \( -2 x \) cannot be combined. She made the first error in Step 4 because the simplified expression is \( -x-5 \).

Kadesha's journey through simplifying that expression is a classic tale of learning through trial and error! When distributing in such expressions, it’s crucial to remember that the signs of the coefficients play an essential role. In Step 1, she correctly identified that negating the first term and distributing the second involves keeping an eye on the signs, avoiding common pitfalls there. In the grand style of math, combining like terms is like a dance! You only want to partner up the terms that are the same type. In Kadesha's case, the mistake lies in assuming that -x and -2x could be simplified together correctly. Instead, -x should simply waltz away with itself, proving that paying attention to coefficients is key in showing off your simplification skills!