Carlos is solving the equation 14x−52=−18

Question

. His solution is as follows.

14x−52
=
−18

+52
+52
Add 52
to both sides.
14x
=
218
−18+52=−18+208=218

4⋅14x
=
4⋅218
Multiply both sides by 4.
x
=
212
4⋅218=212
.
In which part of the solution, if any, did Carlos make the first error?

(1 point)
Responses

He added 52
to both sides.
He added 5 halves to both sides. - no response given

He incorrectly added −18
and 52
.
He incorrectly added negative 1 eighth and 5 halves. - no response given

He did not make any errors.
He did not make any errors. - no response given

He multiplied both sides by 4.

Answer 1

Carlos made the first error when he incorrectly added \(-18\) and \(52\).

Here's the breakdown of the steps:

1. He correctly started with the equation \(14x - 52 = -18\).
2. When he added \(52\) to both sides, he should have computed \(-18 + 52\) correctly. The correct calculation is \(-18 + 52 = 34\), but Carlos arrived at \(218\), which is incorrect.

Thus, he made his first error in the addition step when trying to simplify \( -18 + 52\).