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Answer :
To find the term you need to add to the expression [tex]\(\frac{5}{8}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex], we should focus only on the terms with [tex]\(x\)[/tex].
You want to determine what term, when added to [tex]\(\frac{5}{8}x\)[/tex], makes it equal to [tex]\(\frac{1}{2}x\)[/tex]. Here are the steps to find that term:
1. Start with the equation:
[tex]\[
\frac{5}{8}x + \text{term} = \frac{1}{2}x
\][/tex]
2. To isolate the term, subtract [tex]\(\frac{5}{8}x\)[/tex] from both sides:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{8}x
\][/tex]
3. Now, find a common denominator to subtract these fractions. The common denominator for 2 and 8 is 8.
4. Convert [tex]\(\frac{1}{2}\)[/tex] to a fraction with a denominator of 8:
[tex]\[
\frac{1}{2} = \frac{4}{8}
\][/tex]
5. Now, perform the subtraction:
[tex]\[
\frac{4}{8}x - \frac{5}{8}x = -\frac{1}{8}x
\][/tex]
Therefore, the term you need to add to [tex]\(\frac{5}{8}x - 4\)[/tex] to make it equal to [tex]\(\frac{1}{2}x - 4\)[/tex] is [tex]\(-\frac{1}{8}x\)[/tex].
This term isn't directly listed in the options given, but by checking the closest option, [tex]\(-\frac{1}{3}x\)[/tex] is an option with a negative coefficient that's not exactly correct but matches in form (multiplying by x) and closest to the kind of term we are looking for among given choices. None of the options show the exact term [tex]\(-\frac{1}{8}x\)[/tex], indicating that choice isn't explicitly listed as provided.
You want to determine what term, when added to [tex]\(\frac{5}{8}x\)[/tex], makes it equal to [tex]\(\frac{1}{2}x\)[/tex]. Here are the steps to find that term:
1. Start with the equation:
[tex]\[
\frac{5}{8}x + \text{term} = \frac{1}{2}x
\][/tex]
2. To isolate the term, subtract [tex]\(\frac{5}{8}x\)[/tex] from both sides:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{8}x
\][/tex]
3. Now, find a common denominator to subtract these fractions. The common denominator for 2 and 8 is 8.
4. Convert [tex]\(\frac{1}{2}\)[/tex] to a fraction with a denominator of 8:
[tex]\[
\frac{1}{2} = \frac{4}{8}
\][/tex]
5. Now, perform the subtraction:
[tex]\[
\frac{4}{8}x - \frac{5}{8}x = -\frac{1}{8}x
\][/tex]
Therefore, the term you need to add to [tex]\(\frac{5}{8}x - 4\)[/tex] to make it equal to [tex]\(\frac{1}{2}x - 4\)[/tex] is [tex]\(-\frac{1}{8}x\)[/tex].
This term isn't directly listed in the options given, but by checking the closest option, [tex]\(-\frac{1}{3}x\)[/tex] is an option with a negative coefficient that's not exactly correct but matches in form (multiplying by x) and closest to the kind of term we are looking for among given choices. None of the options show the exact term [tex]\(-\frac{1}{8}x\)[/tex], indicating that choice isn't explicitly listed as provided.
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