Answer :
To solve this problem, we need to find 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].
Let's break down the expressions:
1. Start with the expression [tex]\(\frac{5}{6}x - 4\)[/tex].
2. We want this expression to be equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex].
To achieve this, focus on the [tex]\(x\)[/tex] terms in both expressions because the [tex]\( -4\)[/tex] is already equal:
- First expression: [tex]\(\frac{5}{6}x\)[/tex]
- Second expression: [tex]\(\frac{1}{2}x\)[/tex]
Now, subtract [tex]\(\frac{5}{6}x\)[/tex] from [tex]\(\frac{1}{2}x\)[/tex] to find the difference:
[tex]\[
\frac{1}{2}x - \frac{5}{6}x
\][/tex]
To perform the subtraction, we need a common denominator. The least common denominator of 2 and 6 is 6.
Convert [tex]\(\frac{1}{2}\)[/tex] to have a denominator of 6:
[tex]\[
\frac{1}{2} = \frac{3}{6}
\][/tex]
Now subtract:
[tex]\[
\frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
Simplify [tex]\(-\frac{2}{6}x\)[/tex]:
[tex]\[
-\frac{2}{6}x = -\frac{1}{3}x
\][/tex]
Thus, the term we need to add is [tex]\(-\frac{1}{3}x\)[/tex].
The correct answer is [tex]\(-\frac{1}{3}x\)[/tex].
Let's break down the expressions:
1. Start with the expression [tex]\(\frac{5}{6}x - 4\)[/tex].
2. We want this expression to be equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex].
To achieve this, focus on the [tex]\(x\)[/tex] terms in both expressions because the [tex]\( -4\)[/tex] is already equal:
- First expression: [tex]\(\frac{5}{6}x\)[/tex]
- Second expression: [tex]\(\frac{1}{2}x\)[/tex]
Now, subtract [tex]\(\frac{5}{6}x\)[/tex] from [tex]\(\frac{1}{2}x\)[/tex] to find the difference:
[tex]\[
\frac{1}{2}x - \frac{5}{6}x
\][/tex]
To perform the subtraction, we need a common denominator. The least common denominator of 2 and 6 is 6.
Convert [tex]\(\frac{1}{2}\)[/tex] to have a denominator of 6:
[tex]\[
\frac{1}{2} = \frac{3}{6}
\][/tex]
Now subtract:
[tex]\[
\frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
Simplify [tex]\(-\frac{2}{6}x\)[/tex]:
[tex]\[
-\frac{2}{6}x = -\frac{1}{3}x
\][/tex]
Thus, the term we need to add is [tex]\(-\frac{1}{3}x\)[/tex].
The correct answer is [tex]\(-\frac{1}{3}x\)[/tex].
