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Answer :
To find the term that can be added to the expression [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex], we can follow these steps:
1. Set Up the Equation:
We want to find the term that, when added, makes these two expressions equal. So, the equation is:
[tex]\[
\frac{5}{6}x - 4 + \text{term} = \frac{1}{2}x - 4
\][/tex]
2. Simplify the Equation:
Cancel out the [tex]\(-4\)[/tex] on both sides of the equation, because they are identical and therefore do not affect our expression:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
3. Solve for the Term:
Rearrange the equation to solve for the term by subtracting [tex]\(\frac{5}{6}x\)[/tex] from both sides:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Find a Common Denominator:
To subtract the fractions, first find a common denominator. The least common denominator of 2 and 6 is 6:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
[tex]\[
\frac{5}{6}x = \frac{5}{6}x
\][/tex]
5. Subtract the Fractions:
Now that the fractions have a common denominator, subtract them:
[tex]\[
\text{term} = \frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
6. Simplify the Fraction:
Simplify [tex]\(-\frac{2}{6}\)[/tex] by dividing both the numerator and the denominator by 2:
[tex]\[
\text{term} = -\frac{1}{3}x
\][/tex]
Therefore, the term that can be added to [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex] is [tex]\(-\frac{1}{3}x\)[/tex].
1. Set Up the Equation:
We want to find the term that, when added, makes these two expressions equal. So, the equation is:
[tex]\[
\frac{5}{6}x - 4 + \text{term} = \frac{1}{2}x - 4
\][/tex]
2. Simplify the Equation:
Cancel out the [tex]\(-4\)[/tex] on both sides of the equation, because they are identical and therefore do not affect our expression:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
3. Solve for the Term:
Rearrange the equation to solve for the term by subtracting [tex]\(\frac{5}{6}x\)[/tex] from both sides:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Find a Common Denominator:
To subtract the fractions, first find a common denominator. The least common denominator of 2 and 6 is 6:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
[tex]\[
\frac{5}{6}x = \frac{5}{6}x
\][/tex]
5. Subtract the Fractions:
Now that the fractions have a common denominator, subtract them:
[tex]\[
\text{term} = \frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
6. Simplify the Fraction:
Simplify [tex]\(-\frac{2}{6}\)[/tex] by dividing both the numerator and the denominator by 2:
[tex]\[
\text{term} = -\frac{1}{3}x
\][/tex]
Therefore, the term that can be added to [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex] is [tex]\(-\frac{1}{3}x\)[/tex].
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