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Answer :
To solve this problem, we want to determine which term needs to 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 down the steps:
1. Understand the requirement: We need [tex]\(\frac{5}{6}x - 4 + \text{term} = \frac{1}{2}x - 4\)[/tex].
2. Simplify the equation: Since both sides have a [tex]\(-4\)[/tex], we can remove these from both sides, leaving us with:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
3. Find the term: To find the term, we subtract [tex]\(\frac{5}{6}x\)[/tex] from both sides to solve for the term:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Subtract the fractions: To subtract these fractions, we need a common denominator. The least common denominator of 2 and 6 is 6.
Rewrite [tex]\(\frac{1}{2}x\)[/tex] with a denominator of 6:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
5. Perform the subtraction:
[tex]\[
\frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
6. Simplify the fraction:
[tex]\[
-\frac{2}{6}x = -\frac{1}{3}x
\][/tex]
So, the term that needs to be added is [tex]\(-\frac{1}{3}x\)[/tex]. Therefore, the correct answer is:
[tex]\(-\frac{1}{3}x\)[/tex]
Let's break down the steps:
1. Understand the requirement: We need [tex]\(\frac{5}{6}x - 4 + \text{term} = \frac{1}{2}x - 4\)[/tex].
2. Simplify the equation: Since both sides have a [tex]\(-4\)[/tex], we can remove these from both sides, leaving us with:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
3. Find the term: To find the term, we subtract [tex]\(\frac{5}{6}x\)[/tex] from both sides to solve for the term:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Subtract the fractions: To subtract these fractions, we need a common denominator. The least common denominator of 2 and 6 is 6.
Rewrite [tex]\(\frac{1}{2}x\)[/tex] with a denominator of 6:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
5. Perform the subtraction:
[tex]\[
\frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
6. Simplify the fraction:
[tex]\[
-\frac{2}{6}x = -\frac{1}{3}x
\][/tex]
So, the term that needs to be added is [tex]\(-\frac{1}{3}x\)[/tex]. Therefore, the correct answer is:
[tex]\(-\frac{1}{3}x\)[/tex]
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