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Answer :
To solve the problem of finding what term can be added to [tex]\(\frac{5}{6} x - 4\)[/tex] to make it equivalent to [tex]\(\frac{\overline{2}}{2} x - 4\)[/tex], which simplifies to [tex]\(x - 4\)[/tex], follow these steps:
1. Identify the Expressions:
- The original expression is [tex]\(\frac{5}{6} x - 4\)[/tex].
- The target expression is [tex]\(x - 4\)[/tex].
2. Understand the Objective:
- We need to find a term that, when added to [tex]\(\frac{5}{6} x - 4\)[/tex], will result in [tex]\(x - 4\)[/tex].
3. Set Up the Equation:
- We are looking for a term (let's call it [tex]\(T\)[/tex]) such that:
[tex]\[
\frac{5}{6} x + T = x
\][/tex]
4. Solve for the Term:
- To isolate [tex]\(T\)[/tex], subtract [tex]\(\frac{5}{6} x\)[/tex] from both sides:
[tex]\[
T = x - \frac{5}{6} x
\][/tex]
5. Simplify:
- Rewrite [tex]\(x\)[/tex] as a fraction with the denominator 6, which is [tex]\(\frac{6}{6} x\)[/tex]:
[tex]\[
T = \frac{6}{6} x - \frac{5}{6} x
\][/tex]
- Perform the subtraction:
[tex]\[
T = \left(\frac{6}{6} - \frac{5}{6}\right) x = \frac{1}{6} x
\][/tex]
6. Compare with Options:
- The term [tex]\(\frac{1}{6} x\)[/tex] is closest to [tex]\(\frac{1}{2} x\)[/tex], [tex]\(-\frac{1}{3} x\)[/tex], [tex]\(\frac{1}{2}\)[/tex], and [tex]\(-\frac{1}{3}\)[/tex].
- The closest logical choice respecting fractions is [tex]\(\frac{1}{2} x\)[/tex], with [tex]\(\frac{1}{6} x\)[/tex] being a small fraction of [tex]\(x\)[/tex].
However, if none of the answers exactly match, and considering the operations performed per the given result, none of them are directly aligned numerically because of the calculation steps specifics requested. But based an accurate approach [tex]\(\frac{1}{6} x\)[/tex] is logically more precise.
1. Identify the Expressions:
- The original expression is [tex]\(\frac{5}{6} x - 4\)[/tex].
- The target expression is [tex]\(x - 4\)[/tex].
2. Understand the Objective:
- We need to find a term that, when added to [tex]\(\frac{5}{6} x - 4\)[/tex], will result in [tex]\(x - 4\)[/tex].
3. Set Up the Equation:
- We are looking for a term (let's call it [tex]\(T\)[/tex]) such that:
[tex]\[
\frac{5}{6} x + T = x
\][/tex]
4. Solve for the Term:
- To isolate [tex]\(T\)[/tex], subtract [tex]\(\frac{5}{6} x\)[/tex] from both sides:
[tex]\[
T = x - \frac{5}{6} x
\][/tex]
5. Simplify:
- Rewrite [tex]\(x\)[/tex] as a fraction with the denominator 6, which is [tex]\(\frac{6}{6} x\)[/tex]:
[tex]\[
T = \frac{6}{6} x - \frac{5}{6} x
\][/tex]
- Perform the subtraction:
[tex]\[
T = \left(\frac{6}{6} - \frac{5}{6}\right) x = \frac{1}{6} x
\][/tex]
6. Compare with Options:
- The term [tex]\(\frac{1}{6} x\)[/tex] is closest to [tex]\(\frac{1}{2} x\)[/tex], [tex]\(-\frac{1}{3} x\)[/tex], [tex]\(\frac{1}{2}\)[/tex], and [tex]\(-\frac{1}{3}\)[/tex].
- The closest logical choice respecting fractions is [tex]\(\frac{1}{2} x\)[/tex], with [tex]\(\frac{1}{6} x\)[/tex] being a small fraction of [tex]\(x\)[/tex].
However, if none of the answers exactly match, and considering the operations performed per the given result, none of them are directly aligned numerically because of the calculation steps specifics requested. But based an accurate approach [tex]\(\frac{1}{6} x\)[/tex] is logically more precise.
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