Question

identify the mistake. explain how to correct it.
3(k + 3) - 9k=-24
3k + 9 - 9k=-24
i distributed the 3.
+ 9k + 9k
i added 9k to 3k.
3k+9=-24

• 9 - 9

i subtracted 9 from both sides of the equation.
3k=-33
3k/3=-33/3
i divided both sides of the equation by 3.
k = - 11
a negative divided by a positive is a negative.

Explanation:

Step1: Identify the error in distribution

The original equation is $3(k + 3)-4k=-24$. When distributing the 3, it should be $3k+9 - 4k=-24$, not $3k - 9-4k=-24$. The error was in multiplying 3 and 3 as - 9 instead of 9.

Step2: Correct the distribution and solve

The correct equation after distribution is $3k + 9-4k=-24$. Combine like - terms: $(3k-4k)+9=-24$, which simplifies to $-k + 9=-24$. Subtract 9 from both sides: $-k=-24 - 9=-33$. Multiply both sides by - 1 to solve for k, so $k = 33$.

Answer:

The mistake was incorrect distribution (3 times 3 was calculated as - 9 instead of 9). The correct solution is $k = 33$.