Answer :
To solve the problem of finding 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], follow these steps:
1. Start with the Original Expressions:
- You have [tex]\(\frac{5}{6}x - 4\)[/tex].
- You want this to become [tex]\(\frac{1}{2}x - 4\)[/tex].
2. Identify What Needs to be Changed:
- Both expressions have [tex]\(-4\)[/tex] in common, so you don't need to change anything with the constant term.
3. Focus on the Variable Terms:
- Focus on the coefficient of [tex]\(x\)[/tex]. In the original expression, the coefficient is [tex]\(\frac{5}{6}\)[/tex].
- In the desired expression, the coefficient is [tex]\(\frac{1}{2}\)[/tex].
4. Determine the Difference in Coefficients:
- You need to find the difference between [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex].
- Rewrite [tex]\(\frac{1}{2}\)[/tex] as an equivalent fraction with a denominator of 6:
[tex]\[
\frac{1}{2} = \frac{3}{6}
\][/tex]
- Subtract [tex]\(\frac{5}{6}\)[/tex] from [tex]\(\frac{3}{6}\)[/tex]:
[tex]\[
\frac{3}{6} - \frac{5}{6} = -\frac{2}{6} = -\frac{1}{3}
\][/tex]
5. Result:
- The term you can add to [tex]\(\frac{5}{6}x - 4\)[/tex] is [tex]\(-\frac{1}{3}x\)[/tex].
So, [tex]\(-\frac{1}{3}x\)[/tex] is the correct term to add to make the expressions equivalent.
1. Start with the Original Expressions:
- You have [tex]\(\frac{5}{6}x - 4\)[/tex].
- You want this to become [tex]\(\frac{1}{2}x - 4\)[/tex].
2. Identify What Needs to be Changed:
- Both expressions have [tex]\(-4\)[/tex] in common, so you don't need to change anything with the constant term.
3. Focus on the Variable Terms:
- Focus on the coefficient of [tex]\(x\)[/tex]. In the original expression, the coefficient is [tex]\(\frac{5}{6}\)[/tex].
- In the desired expression, the coefficient is [tex]\(\frac{1}{2}\)[/tex].
4. Determine the Difference in Coefficients:
- You need to find the difference between [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex].
- Rewrite [tex]\(\frac{1}{2}\)[/tex] as an equivalent fraction with a denominator of 6:
[tex]\[
\frac{1}{2} = \frac{3}{6}
\][/tex]
- Subtract [tex]\(\frac{5}{6}\)[/tex] from [tex]\(\frac{3}{6}\)[/tex]:
[tex]\[
\frac{3}{6} - \frac{5}{6} = -\frac{2}{6} = -\frac{1}{3}
\][/tex]
5. Result:
- The term you can add to [tex]\(\frac{5}{6}x - 4\)[/tex] is [tex]\(-\frac{1}{3}x\)[/tex].
So, [tex]\(-\frac{1}{3}x\)[/tex] is the correct term to add to make the expressions equivalent.
