Answer :
To solve the problem of finding the term needed to make the expression [tex]\(\frac{5}{6}x - 4\)[/tex] equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex], we need to focus on the coefficients of [tex]\(x\)[/tex] in both expressions.
1. Identify the Coefficients:
- The coefficient of [tex]\(x\)[/tex] in [tex]\(\frac{5}{6}x - 4\)[/tex] is [tex]\(\frac{5}{6}\)[/tex].
- The coefficient of [tex]\(x\)[/tex] in [tex]\(\frac{1}{2}x - 4\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
2. Calculate the Difference in Coefficients:
- We want to adjust [tex]\(\frac{5}{6}\)[/tex] to be equal to [tex]\(\frac{1}{2}\)[/tex].
- To find the difference, subtract the two coefficients:
[tex]\[
\frac{1}{2} - \frac{5}{6}
\][/tex]
3. Simplify the Difference:
- Convert [tex]\(\frac{1}{2}\)[/tex] to an equivalent fraction with a denominator of 6. This is [tex]\(\frac{3}{6}\)[/tex].
- Now, subtract:
[tex]\[
\frac{3}{6} - \frac{5}{6} = -\frac{2}{6}
\][/tex]
- Simplify [tex]\(-\frac{2}{6}\)[/tex] to [tex]\(-\frac{1}{3}\)[/tex].
4. Conclusion:
- The term you need to 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 term is [tex]\(-\frac{1}{3}x\)[/tex].
1. Identify the Coefficients:
- The coefficient of [tex]\(x\)[/tex] in [tex]\(\frac{5}{6}x - 4\)[/tex] is [tex]\(\frac{5}{6}\)[/tex].
- The coefficient of [tex]\(x\)[/tex] in [tex]\(\frac{1}{2}x - 4\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
2. Calculate the Difference in Coefficients:
- We want to adjust [tex]\(\frac{5}{6}\)[/tex] to be equal to [tex]\(\frac{1}{2}\)[/tex].
- To find the difference, subtract the two coefficients:
[tex]\[
\frac{1}{2} - \frac{5}{6}
\][/tex]
3. Simplify the Difference:
- Convert [tex]\(\frac{1}{2}\)[/tex] to an equivalent fraction with a denominator of 6. This is [tex]\(\frac{3}{6}\)[/tex].
- Now, subtract:
[tex]\[
\frac{3}{6} - \frac{5}{6} = -\frac{2}{6}
\][/tex]
- Simplify [tex]\(-\frac{2}{6}\)[/tex] to [tex]\(-\frac{1}{3}\)[/tex].
4. Conclusion:
- The term you need to 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 term is [tex]\(-\frac{1}{3}x\)[/tex].
