Answer :
To solve this problem, we need to determine what term must be added to the expression [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equal to [tex]\(\frac{1}{2}x - 4\)[/tex].
Let's break it down step-by-step:
1. Set up the equation:
[tex]\[
\left(\frac{5}{6}x - 4\right) + \text{term} = \frac{1}{2}x - 4
\][/tex]
2. Eliminate the [tex]\(-4\)[/tex] on both sides:
Since [tex]\(-4\)[/tex] is present on both sides of the equation, we can cancel it out:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
3. Isolate the term:
Subtract [tex]\(\frac{5}{6}x\)[/tex] from both sides to find the term:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Combine the fractions:
To combine these fractions, we need a common denominator. The least common denominator for 2 and 6 is 6. Convert [tex]\(\frac{1}{2}x\)[/tex] to have a denominator of 6:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
5. Subtract the fractions:
Now we can subtract [tex]\(\frac{5}{6}x\)[/tex] from [tex]\(\frac{3}{6}x\)[/tex]:
[tex]\[
\frac{3}{6}x - \frac{5}{6}x = \frac{-2}{6}x
\][/tex]
6. Simplify the fraction:
Simplify [tex]\(\frac{-2}{6}x\)[/tex] by dividing both the numerator and denominator by 2:
[tex]\[
\frac{-2}{6}x = -\frac{1}{3}x
\][/tex]
So, the term that can be added is [tex]\(-\frac{1}{3}x\)[/tex]. Therefore, the correct answer is [tex]\(-\frac{1}{3}x\)[/tex].
Let's break it down step-by-step:
1. Set up the equation:
[tex]\[
\left(\frac{5}{6}x - 4\right) + \text{term} = \frac{1}{2}x - 4
\][/tex]
2. Eliminate the [tex]\(-4\)[/tex] on both sides:
Since [tex]\(-4\)[/tex] is present on both sides of the equation, we can cancel it out:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
3. Isolate the term:
Subtract [tex]\(\frac{5}{6}x\)[/tex] from both sides to find the term:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Combine the fractions:
To combine these fractions, we need a common denominator. The least common denominator for 2 and 6 is 6. Convert [tex]\(\frac{1}{2}x\)[/tex] to have a denominator of 6:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
5. Subtract the fractions:
Now we can subtract [tex]\(\frac{5}{6}x\)[/tex] from [tex]\(\frac{3}{6}x\)[/tex]:
[tex]\[
\frac{3}{6}x - \frac{5}{6}x = \frac{-2}{6}x
\][/tex]
6. Simplify the fraction:
Simplify [tex]\(\frac{-2}{6}x\)[/tex] by dividing both the numerator and denominator by 2:
[tex]\[
\frac{-2}{6}x = -\frac{1}{3}x
\][/tex]
So, the term that can be added is [tex]\(-\frac{1}{3}x\)[/tex]. Therefore, the correct answer is [tex]\(-\frac{1}{3}x\)[/tex].
