High School

What term can you add to [tex]\frac{5}{6} x - 4[/tex] to make it equivalent to [tex]\frac{1}{2} x - 4[/tex]?

A. [tex]-\frac{1}{3} x[/tex]

B. [tex]-\frac{1}{3}[/tex]

C. [tex]\frac{1}{2} x[/tex]

D. [tex]\frac{1}{2}[/tex]

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].