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QuestionA student found −4+x-4+x for x=−912x=-9 \frac{1}{2} and got 5125 \frac{1}{2}. What was the student's mistake?

Studdy Solution

STEP 1

Assumptions1. The expression to be evaluated is −4+x-4+x . The value of xx is −91-9 \frac{1}{}
3. The student's answer is 515 \frac{1}{}

STEP 2

First, let's substitute the given value of xx into the expression.
−4+x=−4+(−912)-4+x = -4 + (-9 \frac{1}{2})

STEP 3

Now, let's simplify the expression.
−+(−912)=−1312- + (-9 \frac{1}{2}) = -13 \frac{1}{2}

STEP 4

We see that the correct answer should be −1312-13 \frac{1}{2}, not 12 \frac{1}{2}. So, the student made a mistake in the calculation.

STEP 5

To identify the possible error, let's consider what the student might have done to get 5125 \frac{1}{2}.

STEP 6

The student might have mistakenly added 44 to −912-9 \frac{1}{2} instead of subtracting 44.
−4+x=4+(−912)-4 + x =4 + (-9 \frac{1}{2})

STEP 7

If we simplify this incorrect calculation, we get the student's answer.
4+(−912)=−5124 + (-9 \frac{1}{2}) = -5 \frac{1}{2}

STEP 8

However, the student's answer is 5125 \frac{1}{2}, not −512-5 \frac{1}{2}. This suggests that the student might have also made a mistake with the sign, treating −512-5 \frac{1}{2} as 5125 \frac{1}{2}.
In conclusion, the student likely made two mistakes adding instead of subtracting 44 from xx, and ignoring the negative sign of the result.

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