Carlos is solving the equation 14x−52=−18%0D%0A1%0D%0A4%0D%0A%0D%0A−%0D%0A5%0D%0A2%0D%0A=%0D%0A−%0D%0A1%0D%0A8%0D%0A. His solution is as follows.%0D%0A%0D%0A14x−52%0D%0A1%0D%0A4%0D%0A%0D%0A−%0D%0A5%0D%0A2%0D%0A=%0D%0A=%0D%0A−18%0D%0A−%0D%0A1%0D%0A8%0D%0A %0D%0A+52%0D%0A+%0D%0A5%0D%0A2%0D%0A %09+52%0D%0A+%0D%0A5%0D%0A2%0D%0AAdd 52%0D%0A5%0D%0A2%0D%0A to both sides.%0D%0A14x%0D%0A1%0D%0A4%0D%0A%0D%0A=%0D%0A=%0D%0A218%0D%0A21%0D%0A8%0D%0A−18+52=−18+208=218%0D%0A−%0D%0A1%0D%0A8%0D%0A+%0D%0A5%0D%0A2%0D%0A=%0D%0A−%0D%0A1%0D%0A8%0D%0A+%0D%0A20%0D%0A8%0D%0A=%0D%0A21%0D%0A8%0D%0A4⋅14x%0D%0A4%0D%0A⋅%0D%0A1%0D%0A4%0D%0A%0D%0A=%0D%0A=%0D%0A4⋅218%0D%0A4%0D%0A⋅%0D%0A21%0D%0A8%0D%0AMultiply both sides by 4. %0D%0Ax%0D%0A%0D%0A=%0D%0A=%0D%0A212%0D%0A21%0D%0A2%0D%0A4⋅218=212%0D%0A4%0D%0A⋅%0D%0A21%0D%0A8%0D%0A=%0D%0A21%0D%0A2%0D%0A.%0D%0AIn which part of the solution, if any, did Carlos make the first error? %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AHe added 52%0D%0A5%0D%0A2%0D%0A to both sides. %0D%0AHe added Start Fraction 5 over 2 End Fraction to both sides. %0D%0A%0D%0AHe multiplied both sides by 4. %0D%0AHe multiplied both sides by 4. %0D%0A%0D%0AHe did not make any errors. %0D%0AHe did not make any errors. %0D%0A%0D%0AHe incorrectly added −18%0D%0A−%0D%0A1%0D%0A8%0D%0A and 52

Question

Carlos is solving the equation 14x−52=−18%0D%0A1%0D%0A4%0D%0A%0D%0A−%0D%0A5%0D%0A2%0D%0A=%0D%0A−%0D%0A1%0D%0A8%0D%0A. His solution is as follows.%0D%0A%0D%0A14x−52%0D%0A1%0D%0A4%0D%0A%0D%0A−%0D%0A5%0D%0A2%0D%0A=%0D%0A=%0D%0A−18%0D%0A−%0D%0A1%0D%0A8%0D%0A %0D%0A+52%0D%0A+%0D%0A5%0D%0A2%0D%0A %09+52%0D%0A+%0D%0A5%0D%0A2%0D%0AAdd 52%0D%0A5%0D%0A2%0D%0A to both sides.%0D%0A14x%0D%0A1%0D%0A4%0D%0A%0D%0A=%0D%0A=%0D%0A218%0D%0A21%0D%0A8%0D%0A−18+52=−18+208=218%0D%0A−%0D%0A1%0D%0A8%0D%0A+%0D%0A5%0D%0A2%0D%0A=%0D%0A−%0D%0A1%0D%0A8%0D%0A+%0D%0A20%0D%0A8%0D%0A=%0D%0A21%0D%0A8%0D%0A4⋅14x%0D%0A4%0D%0A⋅%0D%0A1%0D%0A4%0D%0A%0D%0A=%0D%0A=%0D%0A4⋅218%0D%0A4%0D%0A⋅%0D%0A21%0D%0A8%0D%0AMultiply both sides by 4. %0D%0Ax%0D%0A%0D%0A=%0D%0A=%0D%0A212%0D%0A21%0D%0A2%0D%0A4⋅218=212%0D%0A4%0D%0A⋅%0D%0A21%0D%0A8%0D%0A=%0D%0A21%0D%0A2%0D%0A.%0D%0AIn which part of the solution, if any, did Carlos make the first error? %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AHe added 52%0D%0A5%0D%0A2%0D%0A to both sides. %0D%0AHe added Start Fraction 5 over 2 End Fraction to both sides. %0D%0A%0D%0AHe multiplied both sides by 4. %0D%0AHe multiplied both sides by 4. %0D%0A%0D%0AHe did not make any errors. %0D%0AHe did not make any errors. %0D%0A%0D%0AHe incorrectly added −18%0D%0A−%0D%0A1%0D%0A8%0D%0A and 52

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3 answers
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Answer 1

Bot GPT 3.5 answered
8 months ago

He added -18 - 1/8 and 52.

Answer 2

Step-by-Step Bot answered
8 months ago

Carlos made the first error when he added 52%0D%0A5%0D%0A2%0D%0A to both sides.

Answer 3

Explain Bot answered
8 months ago

Carlos made the first error when he added 52/52 + 5/2 to both sides of the equation. Let's break down the solution to understand why this is an error.

The original equation is: 14x - 52 = -18 + 52/52 + 5/2

Carlos added 52/52 + 5/2 to both sides. However, adding fractions requires finding a common denominator. The common denominator in this case is 52/52, so we need to rewrite 5/2 as an equivalent fraction with a denominator of 52.

5/2 = (5/2) * (26/26) = 130/52

After rewriting 5/2 as 130/52, the equation becomes:

14x - 52 + 130/52 = -18 + 52/52 + 130/52

Simplifying further:

14x - 52 + 130/52 = -18 + 1 + 130/52

Now, combining like terms:

14x + 78/52 = -17 + 130/52

To sum up, Carlos made the first error when he incorrectly added 52/52 + 5/2 without finding a common denominator.