Question

Angie is solving the equation −x+7=−11
. Her solution is as follows.

−x+7
=
−11

−7
−7
Subtract 7 from both sides.
x
=
−18
−11−7=−18
.
In which part of the solution, if any, did Angie make an error?

Answer 1

Let's walk through Angie's solution step by step:

1. She starts with the equation:
\[
-x + 7 = -11
\]

2. Angie subtracts 7 from both sides:
\[
-x + 7 - 7 = -11 - 7
\]
This simplifies to:
\[
-x = -18
\]
At this point, her operation is correct.

3. Next, she needs to isolate \(x\). To do this, she should multiply both sides of the equation by -1:
\[
x = 18
\]

Instead, Angie did not perform the last step correctly because she incorrectly left \( -x = -18 \) and stated \( x = -18 \). The error occurred when she concluded that \( x = -18 \).

The correct solution is:
\[
x = 18
\]

So, Angie made an error in the final step of her solution.