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Answer :
To solve the problem, we want to determine what term should be added to [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex].
Let's start by setting up the equation:
[tex]\[
\frac{5}{6}x - 4 + \text{term} = \frac{1}{2}x - 4
\][/tex]
Since the "-4" is present on both sides of the equation, they cancel each other out. So, we focus on the [tex]\(x\)[/tex] terms:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
To find the "term," we need to determine what, when added to [tex]\(\frac{5}{6}x\)[/tex], results in [tex]\(\frac{1}{2}x\)[/tex]. Thus, we get:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
Now, we'll subtract the fractions involving [tex]\(x\)[/tex].
First, find a common denominator for [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]. The common denominator is 6. Convert [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{3}{6}\)[/tex]:
[tex]\[
\text{term} = \frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
Simplify [tex]\(-\frac{2}{6}\)[/tex]:
[tex]\[
-\frac{2}{6} = -\frac{1}{3}
\][/tex]
Therefore, the term we need to add is [tex]\(-\frac{1}{3}x\)[/tex].
The correct option from the list is [tex]\(-\frac{1}{3}x\)[/tex].
Let's start by setting up the equation:
[tex]\[
\frac{5}{6}x - 4 + \text{term} = \frac{1}{2}x - 4
\][/tex]
Since the "-4" is present on both sides of the equation, they cancel each other out. So, we focus on the [tex]\(x\)[/tex] terms:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
To find the "term," we need to determine what, when added to [tex]\(\frac{5}{6}x\)[/tex], results in [tex]\(\frac{1}{2}x\)[/tex]. Thus, we get:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
Now, we'll subtract the fractions involving [tex]\(x\)[/tex].
First, find a common denominator for [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex]. The common denominator is 6. Convert [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{3}{6}\)[/tex]:
[tex]\[
\text{term} = \frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
Simplify [tex]\(-\frac{2}{6}\)[/tex]:
[tex]\[
-\frac{2}{6} = -\frac{1}{3}
\][/tex]
Therefore, the term we need to add is [tex]\(-\frac{1}{3}x\)[/tex].
The correct option from the list is [tex]\(-\frac{1}{3}x\)[/tex].
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