Carlos is solving the equation 1/4x−5/2=−1/8

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 did not make any errors.
He did not make any errors.

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

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 .
Remaining Attempts : 3
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Answer 1

To solve the equation \( \frac{1}{4}x - \frac{5}{2} = -\frac{1}{8} \) correctly, let's break down the steps and identify any mistakes in Carlos's solution.

1. Start with the original equation: \[ \frac{1}{4}x - \frac{5}{2} = -\frac{1}{8} \]

2. The first step in solving for \( x \) should be to isolate \( \frac{1}{4}x \). Carlos correctly added \( \frac{5}{2} \) to both sides: \[ \frac{1}{4}x = -\frac{1}{8} + \frac{5}{2} \]

3. Now, convert \( \frac{5}{2} \) to an equivalent fraction with a denominator of 8: \[ \frac{5}{2} = \frac{20}{8} \] Thus, we can substitute this in: \[ -\frac{1}{8} + \frac{20}{8} = \frac{19}{8} \] It follows that: \[ \frac{1}{4}x = \frac{19}{8} \]

4. Next, Carlos multiplied both sides by 4. To do this correctly, he should have written: \[ x = 4 \cdot \frac{19}{8} = \frac{76}{8} = \frac{19}{2} \]

Now, referring to Carlos’s work, let’s highlight where he made an error:

• Mistake Identification: Carlos incorrectly calculated the sum \(-\frac{1}{8} + \frac{5}{2}\), where he should have added \(-\frac{1}{8}\) and \(\frac{20}{8}\), resulting in \(\frac{19}{8}\).

So, the correct answer is: He incorrectly added \( -\frac{1}{8} \) and \( \frac{5}{2} \).