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], we need to look at the expressions' coefficients for [tex]\(x\)[/tex].
1. Start by comparing the coefficients of [tex]\(x\)[/tex] in both expressions. We have:
- The coefficient of [tex]\(x\)[/tex] in the first expression: [tex]\(\frac{5}{6}\)[/tex].
- The coefficient of [tex]\(x\)[/tex] in the second expression: [tex]\(\frac{1}{2}\)[/tex].
2. We need to find the difference between these coefficients to see what needs to be added to [tex]\(\frac{5}{6}x\)[/tex] to make it [tex]\(\frac{1}{2}x\)[/tex].
3. Calculate the difference:
[tex]\[
\text{Needed term} = \frac{1}{2} - \frac{5}{6}
\][/tex]
4. To find this difference, convert [tex]\(\frac{1}{2}\)[/tex] to a fraction with the same denominator as [tex]\(\frac{5}{6}\)[/tex], which is 6:
- [tex]\(\frac{1}{2}\)[/tex] can be rewritten as [tex]\(\frac{3}{6}\)[/tex].
5. Now, subtract the fractions:
[tex]\[
\frac{3}{6} - \frac{5}{6} = -\frac{2}{6}
\][/tex]
6. Simplify [tex]\(-\frac{2}{6}\)[/tex]:
[tex]\[
-\frac{2}{6} = -\frac{1}{3}
\][/tex]
Therefore, the term [tex]\(-\frac{1}{3}x\)[/tex] needs to be added to [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex]. So, the correct choice from the given options is [tex]\(-\frac{1}{3}x\)[/tex].
1. Start by comparing the coefficients of [tex]\(x\)[/tex] in both expressions. We have:
- The coefficient of [tex]\(x\)[/tex] in the first expression: [tex]\(\frac{5}{6}\)[/tex].
- The coefficient of [tex]\(x\)[/tex] in the second expression: [tex]\(\frac{1}{2}\)[/tex].
2. We need to find the difference between these coefficients to see what needs to be added to [tex]\(\frac{5}{6}x\)[/tex] to make it [tex]\(\frac{1}{2}x\)[/tex].
3. Calculate the difference:
[tex]\[
\text{Needed term} = \frac{1}{2} - \frac{5}{6}
\][/tex]
4. To find this difference, convert [tex]\(\frac{1}{2}\)[/tex] to a fraction with the same denominator as [tex]\(\frac{5}{6}\)[/tex], which is 6:
- [tex]\(\frac{1}{2}\)[/tex] can be rewritten as [tex]\(\frac{3}{6}\)[/tex].
5. Now, subtract the fractions:
[tex]\[
\frac{3}{6} - \frac{5}{6} = -\frac{2}{6}
\][/tex]
6. Simplify [tex]\(-\frac{2}{6}\)[/tex]:
[tex]\[
-\frac{2}{6} = -\frac{1}{3}
\][/tex]
Therefore, the term [tex]\(-\frac{1}{3}x\)[/tex] needs to be added to [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex]. So, the correct choice from the given options is [tex]\(-\frac{1}{3}x\)[/tex].
