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Answer :
To solve this problem, we need to determine what term can be added to the expression [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex].
Let's break it down step-by-step:
1. Identify the Expressions:
- We have an expression: [tex]\(\frac{5}{6}x - 4\)[/tex].
- We want it to be equal to: [tex]\(\frac{1}{2}x - 4\)[/tex].
2. Compare the Constant Terms:
- Both expressions have the constant term [tex]\(-4\)[/tex], which is already the same. So, we don't need to change anything regarding the constant term.
3. Compare the Coefficients of [tex]\(x\)[/tex]:
- In the first expression, the coefficient of [tex]\(x\)[/tex] is [tex]\(\frac{5}{6}\)[/tex].
- In the second expression, the coefficient of [tex]\(x\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
4. Determine the Difference in Coefficients:
- To make the coefficients the same, we need to find what to add to [tex]\(\frac{5}{6}\)[/tex] to get [tex]\(\frac{1}{2}\)[/tex].
- This involves finding the difference: [tex]\(\frac{1}{2} - \frac{5}{6}\)[/tex].
5. Calculate the Difference:
- Convert the fractions to have a common denominator:
- [tex]\(\frac{1}{2} = \frac{3}{6}\)[/tex]
- [tex]\(\frac{5}{6}\)[/tex] remains the same.
- Subtract the coefficients: [tex]\(\frac{3}{6} - \frac{5}{6} = -\frac{2}{6}\)[/tex].
- Simplify [tex]\(-\frac{2}{6}\)[/tex] to [tex]\(-\frac{1}{3}\)[/tex].
The term you need to add is [tex]\(-\frac{1}{3}x\)[/tex].
Therefore, the term [tex]\(-\frac{1}{3}x\)[/tex] should be added to the expression [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex]. The correct choice is [tex]\(-\frac{1}{3}x\)[/tex].
Let's break it down step-by-step:
1. Identify the Expressions:
- We have an expression: [tex]\(\frac{5}{6}x - 4\)[/tex].
- We want it to be equal to: [tex]\(\frac{1}{2}x - 4\)[/tex].
2. Compare the Constant Terms:
- Both expressions have the constant term [tex]\(-4\)[/tex], which is already the same. So, we don't need to change anything regarding the constant term.
3. Compare the Coefficients of [tex]\(x\)[/tex]:
- In the first expression, the coefficient of [tex]\(x\)[/tex] is [tex]\(\frac{5}{6}\)[/tex].
- In the second expression, the coefficient of [tex]\(x\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
4. Determine the Difference in Coefficients:
- To make the coefficients the same, we need to find what to add to [tex]\(\frac{5}{6}\)[/tex] to get [tex]\(\frac{1}{2}\)[/tex].
- This involves finding the difference: [tex]\(\frac{1}{2} - \frac{5}{6}\)[/tex].
5. Calculate the Difference:
- Convert the fractions to have a common denominator:
- [tex]\(\frac{1}{2} = \frac{3}{6}\)[/tex]
- [tex]\(\frac{5}{6}\)[/tex] remains the same.
- Subtract the coefficients: [tex]\(\frac{3}{6} - \frac{5}{6} = -\frac{2}{6}\)[/tex].
- Simplify [tex]\(-\frac{2}{6}\)[/tex] to [tex]\(-\frac{1}{3}\)[/tex].
The term you need to add is [tex]\(-\frac{1}{3}x\)[/tex].
Therefore, the term [tex]\(-\frac{1}{3}x\)[/tex] should be added to the expression [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex]. The correct choice is [tex]\(-\frac{1}{3}x\)[/tex].
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