Answer :
To solve the problem of determining what term to add to the expression [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex], follow these steps:
1. Start by Setting Up the Equation:
We want:
[tex]\[
\frac{5}{6}x - 4 + \text{(term)} = \frac{1}{2}x - 4
\][/tex]
2. Remove the Common Term [tex]\( -4 \)[/tex]:
Since both expressions have [tex]\(-4\)[/tex], we can eliminate it from both sides:
[tex]\[
\frac{5}{6}x + \text{(term)} = \frac{1}{2}x
\][/tex]
3. Isolate the Term:
To find out what term to add to [tex]\(\frac{5}{6}x\)[/tex], subtract [tex]\(\frac{5}{6}x\)[/tex] from both sides:
[tex]\[
\text{(term)} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Simplify the Right Side:
Combine the fractions by finding a common denominator:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
So, the equation becomes:
[tex]\[
\text{(term)} = \frac{3}{6}x - \frac{5}{6}x = \left(\frac{3}{6} - \frac{5}{6}\right)x
\][/tex]
5. Calculate the Difference:
Subtract the fractions:
[tex]\[
\frac{3}{6} - \frac{5}{6} = -\frac{2}{6} = -\frac{1}{3}
\][/tex]
So, the term is:
[tex]\[
\text{(term)} = -\frac{1}{3}x
\][/tex]
Thus, the term to be added is [tex]\(-\frac{1}{3}x\)[/tex].
Therefore, the correct answer is [tex]\(-\frac{1}{3}x\)[/tex].
1. Start by Setting Up the Equation:
We want:
[tex]\[
\frac{5}{6}x - 4 + \text{(term)} = \frac{1}{2}x - 4
\][/tex]
2. Remove the Common Term [tex]\( -4 \)[/tex]:
Since both expressions have [tex]\(-4\)[/tex], we can eliminate it from both sides:
[tex]\[
\frac{5}{6}x + \text{(term)} = \frac{1}{2}x
\][/tex]
3. Isolate the Term:
To find out what term to add to [tex]\(\frac{5}{6}x\)[/tex], subtract [tex]\(\frac{5}{6}x\)[/tex] from both sides:
[tex]\[
\text{(term)} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Simplify the Right Side:
Combine the fractions by finding a common denominator:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
So, the equation becomes:
[tex]\[
\text{(term)} = \frac{3}{6}x - \frac{5}{6}x = \left(\frac{3}{6} - \frac{5}{6}\right)x
\][/tex]
5. Calculate the Difference:
Subtract the fractions:
[tex]\[
\frac{3}{6} - \frac{5}{6} = -\frac{2}{6} = -\frac{1}{3}
\][/tex]
So, the term is:
[tex]\[
\text{(term)} = -\frac{1}{3}x
\][/tex]
Thus, the term to be added is [tex]\(-\frac{1}{3}x\)[/tex].
Therefore, the correct answer is [tex]\(-\frac{1}{3}x\)[/tex].
