Answer :
To solve the problem, we need to determine which term can be added to the expression [tex]\(\frac{5}{6}x - 4\)[/tex] so that it becomes equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex].
1. Set up an equation:
We will write an equation where the expression [tex]\(\frac{5}{6}x - 4\)[/tex] plus an unknown term equals [tex]\(\frac{1}{2}x - 4\)[/tex].
[tex]\[
\left(\frac{5}{6}x - 4\right) + \text{term} = \left(\frac{1}{2}x - 4\right)
\][/tex]
2. Eliminate the constants:
Notice that both sides have [tex]\(-4\)[/tex], which means they cancel each other out. We can rewrite it as:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
3. Compare coefficients:
To find the term that changes [tex]\(\frac{5}{6}x\)[/tex] to [tex]\(\frac{1}{2}x\)[/tex], we compare the coefficients of [tex]\(x\)[/tex].
We need to find what term added to [tex]\(\frac{5}{6}x\)[/tex] results in [tex]\(\frac{1}{2}x\)[/tex]. This means:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
4. Solve for the term:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
5. Calculate the term:
To calculate this, we need to find a common denominator. The least common denominator of 6 and 2 is 6.
Convert [tex]\(\frac{1}{2}x\)[/tex] to have the denominator 6:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
Now, subtract [tex]\(\frac{5}{6}x\)[/tex] from [tex]\(\frac{3}{6}x\)[/tex]:
[tex]\[
\frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x = -\frac{1}{3}x
\][/tex]
Thus, the term you need to add is [tex]\(-\frac{1}{3}x\)[/tex]. This makes [tex]\(\frac{5}{6}x - 4\)[/tex] equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex].
So, the correct answer is [tex]\(-\frac{1}{3}x\)[/tex].
1. Set up an equation:
We will write an equation where the expression [tex]\(\frac{5}{6}x - 4\)[/tex] plus an unknown term equals [tex]\(\frac{1}{2}x - 4\)[/tex].
[tex]\[
\left(\frac{5}{6}x - 4\right) + \text{term} = \left(\frac{1}{2}x - 4\right)
\][/tex]
2. Eliminate the constants:
Notice that both sides have [tex]\(-4\)[/tex], which means they cancel each other out. We can rewrite it as:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
3. Compare coefficients:
To find the term that changes [tex]\(\frac{5}{6}x\)[/tex] to [tex]\(\frac{1}{2}x\)[/tex], we compare the coefficients of [tex]\(x\)[/tex].
We need to find what term added to [tex]\(\frac{5}{6}x\)[/tex] results in [tex]\(\frac{1}{2}x\)[/tex]. This means:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
4. Solve for the term:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
5. Calculate the term:
To calculate this, we need to find a common denominator. The least common denominator of 6 and 2 is 6.
Convert [tex]\(\frac{1}{2}x\)[/tex] to have the denominator 6:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
Now, subtract [tex]\(\frac{5}{6}x\)[/tex] from [tex]\(\frac{3}{6}x\)[/tex]:
[tex]\[
\frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x = -\frac{1}{3}x
\][/tex]
Thus, the term you need to add is [tex]\(-\frac{1}{3}x\)[/tex]. This makes [tex]\(\frac{5}{6}x - 4\)[/tex] equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex].
So, the correct answer is [tex]\(-\frac{1}{3}x\)[/tex].
