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Answer :
To solve the problem of finding a term that can be added to [tex]\(\frac{5}{6} x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2} x - 4\)[/tex], we need to focus on the coefficients of [tex]\(x\)[/tex].
Here are the steps:
1. Identify the Coefficients of [tex]\(x\)[/tex]:
- In the expression [tex]\(\frac{5}{6} x - 4\)[/tex], the coefficient of [tex]\(x\)[/tex] is [tex]\(\frac{5}{6}\)[/tex].
- In the expression [tex]\(\frac{1}{2} x - 4\)[/tex], the coefficient of [tex]\(x\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
2. Calculate the Difference:
- To make the first expression equivalent to the second, we need the coefficients of [tex]\(x\)[/tex] to be the same.
- Find the difference between these coefficients:
[tex]\[
\frac{1}{2} - \frac{5}{6}
\][/tex]
3. Convert to a Common Denominator:
- Convert [tex]\(\frac{1}{2}\)[/tex] to have a denominator of 6:
[tex]\[
\frac{1}{2} = \frac{3}{6}
\][/tex]
4. Calculate the Difference:
- Now calculate [tex]\(\frac{3}{6} - \frac{5}{6}\)[/tex]:
[tex]\[
\frac{3}{6} - \frac{5}{6} = \frac{3 - 5}{6} = \frac{-2}{6} = -\frac{1}{3}
\][/tex]
5. Conclusion:
- The term that needs to be added to [tex]\(\frac{5}{6} x - 4\)[/tex] to equate it with [tex]\(\frac{1}{2} x - 4\)[/tex] is [tex]\(-\frac{1}{3} x\)[/tex].
So, the correct answer is [tex]\(-\frac{1}{3} x\)[/tex].
Here are the steps:
1. Identify the Coefficients of [tex]\(x\)[/tex]:
- In the expression [tex]\(\frac{5}{6} x - 4\)[/tex], the coefficient of [tex]\(x\)[/tex] is [tex]\(\frac{5}{6}\)[/tex].
- In the expression [tex]\(\frac{1}{2} x - 4\)[/tex], the coefficient of [tex]\(x\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
2. Calculate the Difference:
- To make the first expression equivalent to the second, we need the coefficients of [tex]\(x\)[/tex] to be the same.
- Find the difference between these coefficients:
[tex]\[
\frac{1}{2} - \frac{5}{6}
\][/tex]
3. Convert to a Common Denominator:
- Convert [tex]\(\frac{1}{2}\)[/tex] to have a denominator of 6:
[tex]\[
\frac{1}{2} = \frac{3}{6}
\][/tex]
4. Calculate the Difference:
- Now calculate [tex]\(\frac{3}{6} - \frac{5}{6}\)[/tex]:
[tex]\[
\frac{3}{6} - \frac{5}{6} = \frac{3 - 5}{6} = \frac{-2}{6} = -\frac{1}{3}
\][/tex]
5. Conclusion:
- The term that needs to be added to [tex]\(\frac{5}{6} x - 4\)[/tex] to equate it with [tex]\(\frac{1}{2} x - 4\)[/tex] is [tex]\(-\frac{1}{3} x\)[/tex].
So, the correct answer is [tex]\(-\frac{1}{3} x\)[/tex].
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