Answer :
To solve this problem, we need to determine the term that, when added to the expression [tex]\(\frac{5}{6}x - 4\)[/tex], will make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex].
Here's a step-by-step explanation:
1. Understand the Goal: We want to make [tex]\(\frac{5}{6}x - 4\)[/tex] equal to [tex]\(\frac{1}{2}x - 4\)[/tex].
2. Set the Expressions Equal: Start by writing the equation of the two expressions:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
3. Solve for the Term: To find the term that we need to add, subtract [tex]\(\frac{5}{6}x\)[/tex] from [tex]\(\frac{1}{2}x\)[/tex]:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Calculate the Difference: To subtract these fractions, find a common denominator. The least common denominator of 2 and 6 is 6:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
5. Perform the Subtraction:
[tex]\[
\frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
6. Simplify the Result:
[tex]\[
-\frac{2}{6}x = -\frac{1}{3}x
\][/tex]
Thus, the term you need to add is [tex]\(-\frac{1}{3}x\)[/tex]. Therefore, the correct answer is:
[tex]\[
-\frac{1}{3}x
\][/tex]
Here's a step-by-step explanation:
1. Understand the Goal: We want to make [tex]\(\frac{5}{6}x - 4\)[/tex] equal to [tex]\(\frac{1}{2}x - 4\)[/tex].
2. Set the Expressions Equal: Start by writing the equation of the two expressions:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
3. Solve for the Term: To find the term that we need to add, subtract [tex]\(\frac{5}{6}x\)[/tex] from [tex]\(\frac{1}{2}x\)[/tex]:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Calculate the Difference: To subtract these fractions, find a common denominator. The least common denominator of 2 and 6 is 6:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
5. Perform the Subtraction:
[tex]\[
\frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
6. Simplify the Result:
[tex]\[
-\frac{2}{6}x = -\frac{1}{3}x
\][/tex]
Thus, the term you need to add is [tex]\(-\frac{1}{3}x\)[/tex]. Therefore, the correct answer is:
[tex]\[
-\frac{1}{3}x
\][/tex]
