Answer :
To determine which term can be added to [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex], follow these steps:
1. Understand the Problem:
We are looking to make the two expressions equivalent:
[tex]\[
\frac{5}{6}x - 4 + \text{term} = \frac{1}{2}x - 4
\][/tex]
2. Remove the Common Part:
Both expressions have [tex]\(-4\)[/tex], so you can ignore it for now to simplify the problem:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
3. Solve for the Missing Term:
To find the term, subtract [tex]\(\frac{5}{6}x\)[/tex] from both sides:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Calculate the Difference:
Convert [tex]\(\frac{1}{2}x\)[/tex] to have a common denominator with [tex]\(\frac{5}{6}x\)[/tex]. The common denominator for 2 and 6 is 6. So, [tex]\(\frac{1}{2}x\)[/tex] becomes [tex]\(\frac{3}{6}x\)[/tex].
Now, subtract:
[tex]\[
\text{term} = \frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
5. Simplify the Term:
Simplify [tex]\(-\frac{2}{6}x\)[/tex]:
[tex]\[
\text{term} = -\frac{1}{3}x
\][/tex]
So, the term you can add to [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex] is [tex]\(-\frac{1}{3}x\)[/tex]. Therefore, the correct answer is:
[tex]\(-\frac{1}{3}x\)[/tex]
1. Understand the Problem:
We are looking to make the two expressions equivalent:
[tex]\[
\frac{5}{6}x - 4 + \text{term} = \frac{1}{2}x - 4
\][/tex]
2. Remove the Common Part:
Both expressions have [tex]\(-4\)[/tex], so you can ignore it for now to simplify the problem:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
3. Solve for the Missing Term:
To find the term, subtract [tex]\(\frac{5}{6}x\)[/tex] from both sides:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Calculate the Difference:
Convert [tex]\(\frac{1}{2}x\)[/tex] to have a common denominator with [tex]\(\frac{5}{6}x\)[/tex]. The common denominator for 2 and 6 is 6. So, [tex]\(\frac{1}{2}x\)[/tex] becomes [tex]\(\frac{3}{6}x\)[/tex].
Now, subtract:
[tex]\[
\text{term} = \frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
5. Simplify the Term:
Simplify [tex]\(-\frac{2}{6}x\)[/tex]:
[tex]\[
\text{term} = -\frac{1}{3}x
\][/tex]
So, the term you can add to [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex] is [tex]\(-\frac{1}{3}x\)[/tex]. Therefore, the correct answer is:
[tex]\(-\frac{1}{3}x\)[/tex]
