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Answer :
To find the 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 can follow these steps:
1. Set up the equation:
We want to find a term [tex]\(t\)[/tex] such that when added to [tex]\(\frac{5}{6}x - 4\)[/tex], the result is equal to [tex]\(\frac{1}{2}x - 4\)[/tex].
[tex]\[
\frac{5}{6}x - 4 + t = \frac{1}{2}x - 4
\][/tex]
2. Remove constant terms (both sides):
Since both sides have [tex]\(-4\)[/tex], we subtract [tex]\(-4\)[/tex] from both sides to simplify:
[tex]\[
\frac{5}{6}x + t = \frac{1}{2}x
\][/tex]
3. Solve for [tex]\(t\)[/tex]:
To find [tex]\(t\)[/tex], we need to solve for the difference between the coefficients of [tex]\(x\)[/tex].
[tex]\[
t = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Combine the coefficients:
We need a common denominator to subtract [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]. The least common denominator of 2 and 6 is 6.
- [tex]\(\frac{1}{2}x\)[/tex] can be expressed as [tex]\(\frac{3}{6}x\)[/tex].
Substituting these into the equation:
[tex]\[
t = \frac{3}{6}x - \frac{5}{6}x
\][/tex]
5. Calculate:
Subtract the fractions:
[tex]\[
t = \left( \frac{3}{6} - \frac{5}{6} \right) x = \frac{3 - 5}{6}x = -\frac{2}{6}x = -\frac{1}{3}x
\][/tex]
Therefore, the term you need to add is [tex]\(-\frac{1}{3}x\)[/tex].
1. Set up the equation:
We want to find a term [tex]\(t\)[/tex] such that when added to [tex]\(\frac{5}{6}x - 4\)[/tex], the result is equal to [tex]\(\frac{1}{2}x - 4\)[/tex].
[tex]\[
\frac{5}{6}x - 4 + t = \frac{1}{2}x - 4
\][/tex]
2. Remove constant terms (both sides):
Since both sides have [tex]\(-4\)[/tex], we subtract [tex]\(-4\)[/tex] from both sides to simplify:
[tex]\[
\frac{5}{6}x + t = \frac{1}{2}x
\][/tex]
3. Solve for [tex]\(t\)[/tex]:
To find [tex]\(t\)[/tex], we need to solve for the difference between the coefficients of [tex]\(x\)[/tex].
[tex]\[
t = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Combine the coefficients:
We need a common denominator to subtract [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]. The least common denominator of 2 and 6 is 6.
- [tex]\(\frac{1}{2}x\)[/tex] can be expressed as [tex]\(\frac{3}{6}x\)[/tex].
Substituting these into the equation:
[tex]\[
t = \frac{3}{6}x - \frac{5}{6}x
\][/tex]
5. Calculate:
Subtract the fractions:
[tex]\[
t = \left( \frac{3}{6} - \frac{5}{6} \right) x = \frac{3 - 5}{6}x = -\frac{2}{6}x = -\frac{1}{3}x
\][/tex]
Therefore, the term you need to add is [tex]\(-\frac{1}{3}x\)[/tex].
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