Answer :
To solve the problem, let's find the term we need to add to [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex].
1. Start with the given expressions:
- Original expression: [tex]\(\frac{5}{6}x - 4\)[/tex]
- Equivalent expression: [tex]\(\frac{1}{2}x - 4\)[/tex]
2. Our goal is to find a term [tex]\(a\)[/tex] that we can add to [tex]\(\frac{5}{6}x - 4\)[/tex] so that the result is equal to [tex]\(\frac{1}{2}x - 4\)[/tex].
3. Set up the equation:
[tex]\[
\frac{5}{6}x - 4 + a = \frac{1}{2}x - 4
\][/tex]
4. Eliminate [tex]\(-4\)[/tex] from both sides of the equation by adding 4 to both sides:
[tex]\[
\frac{5}{6}x + a = \frac{1}{2}x
\][/tex]
5. To find [tex]\(a\)[/tex], subtract [tex]\(\frac{5}{6}x\)[/tex] from both sides:
[tex]\[
a = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
6. Solve the expression [tex]\(\frac{1}{2}x - \frac{5}{6}x\)[/tex]:
- Convert [tex]\(\frac{1}{2}\)[/tex] to a fraction with a denominator of 6, which is [tex]\(\frac{3}{6}x\)[/tex].
- Now, subtract: [tex]\(\frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x\)[/tex].
7. Simplify [tex]\(-\frac{2}{6}x\)[/tex] by dividing both the numerator and the denominator by 2:
[tex]\[
a = -\frac{1}{3}x
\][/tex]
The term you need to add to make the expressions equivalent is [tex]\(-\frac{1}{3}x\)[/tex]. Therefore, the correct answer is [tex]\( -\frac{1}{3}x \)[/tex].
1. Start with the given expressions:
- Original expression: [tex]\(\frac{5}{6}x - 4\)[/tex]
- Equivalent expression: [tex]\(\frac{1}{2}x - 4\)[/tex]
2. Our goal is to find a term [tex]\(a\)[/tex] that we can add to [tex]\(\frac{5}{6}x - 4\)[/tex] so that the result is equal to [tex]\(\frac{1}{2}x - 4\)[/tex].
3. Set up the equation:
[tex]\[
\frac{5}{6}x - 4 + a = \frac{1}{2}x - 4
\][/tex]
4. Eliminate [tex]\(-4\)[/tex] from both sides of the equation by adding 4 to both sides:
[tex]\[
\frac{5}{6}x + a = \frac{1}{2}x
\][/tex]
5. To find [tex]\(a\)[/tex], subtract [tex]\(\frac{5}{6}x\)[/tex] from both sides:
[tex]\[
a = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
6. Solve the expression [tex]\(\frac{1}{2}x - \frac{5}{6}x\)[/tex]:
- Convert [tex]\(\frac{1}{2}\)[/tex] to a fraction with a denominator of 6, which is [tex]\(\frac{3}{6}x\)[/tex].
- Now, subtract: [tex]\(\frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x\)[/tex].
7. Simplify [tex]\(-\frac{2}{6}x\)[/tex] by dividing both the numerator and the denominator by 2:
[tex]\[
a = -\frac{1}{3}x
\][/tex]
The term you need to add to make the expressions equivalent is [tex]\(-\frac{1}{3}x\)[/tex]. Therefore, the correct answer is [tex]\( -\frac{1}{3}x \)[/tex].
