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 Start Fraction 5 over 2 End Fraction to both sides.

He incorrectly added −18
and 52
.
He incorrectly added negative Start Fraction 1 over 8 End Fraction and Start Fraction 5 over 2 End Fraction .

He multiplied both sides by 4.
He multiplied both sides by 4.

He did not make any errors.

Answer 1

Carlos made an error in the step where he added \(-18\) and \(52\).

In his solution, he correctly starts with the equation:

\[ 14x - 52 = -18 \]

When he adds \(52\) to both sides, he gets:

\[ 14x = -18 + 52 \]

However, the correct calculation for \(-18 + 52\) should be:

\[-18 + 52 = 34,\]

not \(218\) as he claimed.

So the correct answer is:

He incorrectly added \(-18\) and \(52\).