Answer :
To solve the problem of finding out which term 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 it down step-by-step:
1. Set Up the Equation:
We are asked to determine what term, when added to [tex]\(\frac{5}{6} x - 4\)[/tex], results in [tex]\(\frac{1}{2} x - 4\)[/tex]. This can be written as:
[tex]\[
\frac{5}{6} x - 4 + \text{(term)} = \frac{1}{2} x - 4
\][/tex]
2. Focus on the [tex]\(x\)[/tex] Terms:
Since the constant terms (-4) on both sides of the equation cancel each other out, we only need to focus on the terms with [tex]\(x\)[/tex]:
[tex]\[
\frac{5}{6} x + \text{(term)} = \frac{1}{2} x
\][/tex]
3. Solve for the Unknown Term:
To find the unknown term that needs to be added, subtract [tex]\(\frac{5}{6} x\)[/tex] from both sides:
[tex]\[
\text{(term)} = \frac{1}{2} x - \frac{5}{6} x
\][/tex]
4. Subtract the Fractions:
To subtract [tex]\(\frac{1}{2} x\)[/tex] and [tex]\(\frac{5}{6} x\)[/tex], make sure they have a common denominator. Since 6 is a common denominator for 2 and 6, convert [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{3}{6}\)[/tex]:
[tex]\[
\text{(term)} = \frac{3}{6} x - \frac{5}{6} x
\][/tex]
5. Simplify the Expression:
Subtracting the fractions:
[tex]\[
\text{(term)} = \left(\frac{3}{6} - \frac{5}{6}\right)x = \frac{-2}{6} x
\][/tex]
Simplify [tex]\(\frac{-2}{6}\)[/tex] to [tex]\(-\frac{1}{3}\)[/tex]:
[tex]\[
\text{(term)} = -\frac{1}{3} x
\][/tex]
Thus, the term that you can add is [tex]\(-\frac{1}{3} x\)[/tex].
1. Set Up the Equation:
We are asked to determine what term, when added to [tex]\(\frac{5}{6} x - 4\)[/tex], results in [tex]\(\frac{1}{2} x - 4\)[/tex]. This can be written as:
[tex]\[
\frac{5}{6} x - 4 + \text{(term)} = \frac{1}{2} x - 4
\][/tex]
2. Focus on the [tex]\(x\)[/tex] Terms:
Since the constant terms (-4) on both sides of the equation cancel each other out, we only need to focus on the terms with [tex]\(x\)[/tex]:
[tex]\[
\frac{5}{6} x + \text{(term)} = \frac{1}{2} x
\][/tex]
3. Solve for the Unknown Term:
To find the unknown term that needs to be added, subtract [tex]\(\frac{5}{6} x\)[/tex] from both sides:
[tex]\[
\text{(term)} = \frac{1}{2} x - \frac{5}{6} x
\][/tex]
4. Subtract the Fractions:
To subtract [tex]\(\frac{1}{2} x\)[/tex] and [tex]\(\frac{5}{6} x\)[/tex], make sure they have a common denominator. Since 6 is a common denominator for 2 and 6, convert [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{3}{6}\)[/tex]:
[tex]\[
\text{(term)} = \frac{3}{6} x - \frac{5}{6} x
\][/tex]
5. Simplify the Expression:
Subtracting the fractions:
[tex]\[
\text{(term)} = \left(\frac{3}{6} - \frac{5}{6}\right)x = \frac{-2}{6} x
\][/tex]
Simplify [tex]\(\frac{-2}{6}\)[/tex] to [tex]\(-\frac{1}{3}\)[/tex]:
[tex]\[
\text{(term)} = -\frac{1}{3} x
\][/tex]
Thus, the term that you can add is [tex]\(-\frac{1}{3} x\)[/tex].
