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

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

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

She did not divide both sides by −1
.

Answer 1

Angie made an error in the step where she is supposed to isolate \( x \). Here's the breakdown:

Starting with the equation: \[ -x + 7 = -11 \]

When she subtracts 7 from both sides, she does it correctly: \[ -x = -11 - 7 \] This simplifies to: \[ -x = -18 \]

Next, when she concludes that \( x = -18 \), there is an error in how she arrived at this conclusion. To isolate \( x \), she should multiply both sides by -1 or simply recognize that \( -x = -18 \) means \( x = 18 \).

Thus, the correct conclusion should have been: \[ x = 18 \]

So, the option that captures her mistake is: She did not divide both sides by −1.