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Answer :
To solve this problem, we want to make the two expressions [tex]\(\frac{5}{6}x - 4\)[/tex] and [tex]\(\frac{1}{2}x - 4\)[/tex] equivalent by adding a term to the first expression.
1. Identify the Parts to Compare:
- Both expressions have the constant term [tex]\(-4\)[/tex], which is already the same, so we can ignore it for the purpose of adding a term.
- Focus on comparing the coefficients of [tex]\(x\)[/tex] in the two expressions: [tex]\(\frac{5}{6}x\)[/tex] and [tex]\(\frac{1}{2}x\)[/tex].
2. Find the Difference in Coefficients:
- Find the difference between the coefficients of [tex]\(x\)[/tex]: [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex].
- To do this, subtract the coefficient of the first expression from the coefficient of the second expression:
[tex]\[
\frac{1}{2} - \frac{5}{6}
\][/tex]
- To subtract these fractions, first find a common denominator. The least common denominator for 2 and 6 is 6.
- Convert [tex]\(\frac{1}{2}\)[/tex] to a fraction with a denominator of 6:
[tex]\[
\frac{1}{2} = \frac{3}{6}
\][/tex]
- The subtraction becomes:
[tex]\[
\frac{3}{6} - \frac{5}{6} = -\frac{2}{6} = -\frac{1}{3}
\][/tex]
3. Determine the Term to Add:
- The term you need to add 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].
Therefore, the correct term to add is [tex]\(-\frac{1}{3}x\)[/tex].
1. Identify the Parts to Compare:
- Both expressions have the constant term [tex]\(-4\)[/tex], which is already the same, so we can ignore it for the purpose of adding a term.
- Focus on comparing the coefficients of [tex]\(x\)[/tex] in the two expressions: [tex]\(\frac{5}{6}x\)[/tex] and [tex]\(\frac{1}{2}x\)[/tex].
2. Find the Difference in Coefficients:
- Find the difference between the coefficients of [tex]\(x\)[/tex]: [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{5}{6}\)[/tex].
- To do this, subtract the coefficient of the first expression from the coefficient of the second expression:
[tex]\[
\frac{1}{2} - \frac{5}{6}
\][/tex]
- To subtract these fractions, first find a common denominator. The least common denominator for 2 and 6 is 6.
- Convert [tex]\(\frac{1}{2}\)[/tex] to a fraction with a denominator of 6:
[tex]\[
\frac{1}{2} = \frac{3}{6}
\][/tex]
- The subtraction becomes:
[tex]\[
\frac{3}{6} - \frac{5}{6} = -\frac{2}{6} = -\frac{1}{3}
\][/tex]
3. Determine the Term to Add:
- The term you need to add 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].
Therefore, the correct term to add is [tex]\(-\frac{1}{3}x\)[/tex].
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