Angie is solving the equation −x+7=−11

Question

. 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 divide both sides by −1
.
She did not divide both sides by negative 1 .

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

She did not make any errors.

Answer 1

Let's break down Angie's solution step by step:

1. The original equation is:
   \(-x + 7 = -11\)

2. Angie attempts to isolate \(x\) by subtracting \(7\) from both sides: \(-x + 7 - 7 = -11 - 7\)

   This simplifies to:
   \(-x = -18\)

3. Next, to solve for \(x\), she should multiply or divide both sides by \(-1\): \(x = 18\)

Now, looking at Angie's conclusion, she mistakenly thinks that \((-11) - 7\) equals \(-18\). Actually, \(-11 - 7\) equals \(-18\) is correct.

The actual mistake Angie made was not dividing both sides by \(-1\) after isolating \(-x\). Hence the correct statement is:

She did not divide both sides by \(-1\).