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?

(1 point)
Responses

She subtracted −11
and −7
incorrectly.
She subtracted negative 11 and negative 7 incorrectly.

She did not make any errors.
She did not make any errors.

She subtracted 7 from both sides.
She subtracted 7 from both sides.

She did not divide both sides by −1
.
She did not divide both sides by negative 1 .
Remaining Attempts : 3
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Answer 1

Let's go through Angie's solution step by step.

The original equation is:
\[
-x + 7 = -11
\]

1. **Subtract 7 from both sides:**
\[
-x + 7 - 7 = -11 - 7
\]
This simplifies to:
\[
-x = -18
\]

2. **To solve for \(x\), multiply both sides by -1 (or divide by -1):**
\[
x = 18
\]

Angie's final answer states \( x = -18 \), which is incorrect.

Her error occurs specifically in the subtraction step where she incorrectly calculates:
\[
-11 - 7 = -18
\]
This should actually be:
\[
-11 - 7 = -18
\]
indicating that she set the left-hand side of the equation \( -x = -18 \) correctly, which actually leads to \( x = 18 \).

So the correct response to identify the error is:
**She did not divide both sides by −1.**

Thus, the error in her calculation comes from not correctly converting \( -x = -18 \) to \( x = 18 \).