Answer :
To solve this problem, we need to determine what term can be added to [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex].
Let's break this down step-by-step:
1. Understanding the Problem:
- We have the expression [tex]\(\frac{5}{6}x - 4\)[/tex].
- We want this to equal [tex]\(\frac{1}{2}x - 4\)[/tex] when a certain term is added.
2. Set Up the Equation:
- To solve for the unknown term, we can set up the following equation:
[tex]\[
\frac{5}{6}x - 4 + (\text{unknown term}) = \frac{1}{2}x - 4
\][/tex]
3. Simplify the Equation:
- Since the constant terms (-4) on both sides of the equation are the same, they cancel each other out. We can focus only on the terms involving [tex]\(x\)[/tex]:
[tex]\[
\frac{5}{6}x + (\text{unknown term}) = \frac{1}{2}x
\][/tex]
4. Solve for the Unknown Term:
- To find the unknown term, we need to determine what must be added to [tex]\(\frac{5}{6}x\)[/tex] to get [tex]\(\frac{1}{2}x\)[/tex].
- Subtract [tex]\(\frac{5}{6}x\)[/tex] from [tex]\(\frac{1}{2}x\)[/tex]:
[tex]\[
\text{unknown term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
5. Calculate the Difference:
- We need a common denominator to subtract the fractions. The least common denominator of 2 and 6 is 6.
- Rewrite [tex]\(\frac{1}{2}x\)[/tex] as [tex]\(\frac{3}{6}x\)[/tex]:
[tex]\[
\frac{3}{6}x - \frac{5}{6}x = \left( \frac{3 - 5}{6} \right) x = -\frac{2}{6}x = -\frac{1}{3}x
\][/tex]
6. Identify the Correct Option:
- The term that needs to be added to make these expressions equivalent is [tex]\(-\frac{1}{3}x\)[/tex].
Therefore, the correct term to add is [tex]\(-\frac{1}{3}x\)[/tex].
Let's break this down step-by-step:
1. Understanding the Problem:
- We have the expression [tex]\(\frac{5}{6}x - 4\)[/tex].
- We want this to equal [tex]\(\frac{1}{2}x - 4\)[/tex] when a certain term is added.
2. Set Up the Equation:
- To solve for the unknown term, we can set up the following equation:
[tex]\[
\frac{5}{6}x - 4 + (\text{unknown term}) = \frac{1}{2}x - 4
\][/tex]
3. Simplify the Equation:
- Since the constant terms (-4) on both sides of the equation are the same, they cancel each other out. We can focus only on the terms involving [tex]\(x\)[/tex]:
[tex]\[
\frac{5}{6}x + (\text{unknown term}) = \frac{1}{2}x
\][/tex]
4. Solve for the Unknown Term:
- To find the unknown term, we need to determine what must be added to [tex]\(\frac{5}{6}x\)[/tex] to get [tex]\(\frac{1}{2}x\)[/tex].
- Subtract [tex]\(\frac{5}{6}x\)[/tex] from [tex]\(\frac{1}{2}x\)[/tex]:
[tex]\[
\text{unknown term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
5. Calculate the Difference:
- We need a common denominator to subtract the fractions. The least common denominator of 2 and 6 is 6.
- Rewrite [tex]\(\frac{1}{2}x\)[/tex] as [tex]\(\frac{3}{6}x\)[/tex]:
[tex]\[
\frac{3}{6}x - \frac{5}{6}x = \left( \frac{3 - 5}{6} \right) x = -\frac{2}{6}x = -\frac{1}{3}x
\][/tex]
6. Identify the Correct Option:
- The term that needs to be added to make these expressions equivalent is [tex]\(-\frac{1}{3}x\)[/tex].
Therefore, the correct term to add is [tex]\(-\frac{1}{3}x\)[/tex].
