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Answer :
To solve this problem, we need to find a term that can be added to the expression [tex]\(\frac{5}{6}x - 4\)[/tex] in order to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex]. Here's how we can figure it out step-by-step:
1. Understand the Objective: We want to make the expressions [tex]\(\frac{5}{6}x - 4\)[/tex] and [tex]\(\frac{1}{2}x - 4\)[/tex] equal by adding a term to the first expression.
2. Set up the Equation:
[tex]\[
\left(\frac{5}{6}x - 4\right) + \text{term} = \frac{1}{2}x - 4
\][/tex]
3. Focus on the [tex]\(x\)[/tex] Terms: Since both expressions have [tex]\(-4\)[/tex], we only need to balance the [tex]\(x\)[/tex] parts:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
4. Isolate the Term: Subtract [tex]\(\frac{5}{6}x\)[/tex] from both sides of the equation to solve for the term:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
5. Calculate the Term: To subtract these fractions, get a common denominator. The common denominator of 2 and 6 is 6:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
[tex]\[
\text{term} = \frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x = -\frac{1}{3}x
\][/tex]
6. Identify the Correct Term: From the list of options, [tex]\(-\frac{1}{3}x\)[/tex] matches our calculated term.
Therefore, the term [tex]\(-\frac{1}{3}x\)[/tex] can be added to [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex].
1. Understand the Objective: We want to make the expressions [tex]\(\frac{5}{6}x - 4\)[/tex] and [tex]\(\frac{1}{2}x - 4\)[/tex] equal by adding a term to the first expression.
2. Set up the Equation:
[tex]\[
\left(\frac{5}{6}x - 4\right) + \text{term} = \frac{1}{2}x - 4
\][/tex]
3. Focus on the [tex]\(x\)[/tex] Terms: Since both expressions have [tex]\(-4\)[/tex], we only need to balance the [tex]\(x\)[/tex] parts:
[tex]\[
\frac{5}{6}x + \text{term} = \frac{1}{2}x
\][/tex]
4. Isolate the Term: Subtract [tex]\(\frac{5}{6}x\)[/tex] from both sides of the equation to solve for the term:
[tex]\[
\text{term} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
5. Calculate the Term: To subtract these fractions, get a common denominator. The common denominator of 2 and 6 is 6:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
[tex]\[
\text{term} = \frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x = -\frac{1}{3}x
\][/tex]
6. Identify the Correct Term: From the list of options, [tex]\(-\frac{1}{3}x\)[/tex] matches our calculated term.
Therefore, the term [tex]\(-\frac{1}{3}x\)[/tex] can be added to [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex].
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