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Answer :
To make the expression [tex]\(\frac{5}{6}x - 4\)[/tex] equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex], we need to find what term can be added to [tex]\(\frac{5}{6}x - 4\)[/tex].
Let's compare the two expressions:
1. [tex]\(\frac{5}{6}x - 4\)[/tex]
2. [tex]\(\frac{1}{2}x - 4\)[/tex]
Notice that the constant term [tex]\(-4\)[/tex] is the same in both expressions. This means we only need to focus on the coefficients of [tex]\(x\)[/tex].
Now, let's find the difference between the coefficients of [tex]\(x\)[/tex] in the two expressions. The coefficient of [tex]\(x\)[/tex] in the first expression is [tex]\(\frac{5}{6}\)[/tex], and in the second expression, it is [tex]\(\frac{1}{2}\)[/tex].
To find what term should be added to [tex]\(\frac{5}{6}x\)[/tex] to make it [tex]\(\frac{1}{2}x\)[/tex], calculate:
[tex]\[
\frac{1}{2} - \frac{5}{6}
\][/tex]
To subtract these fractions, find a common denominator. The common denominator for 2 and 6 is 6:
- Convert [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{3}{6}\)[/tex] (because [tex]\(\frac{1 \times 3}{2 \times 3} = \frac{3}{6}\)[/tex]).
- [tex]\(\frac{5}{6}\)[/tex] stays the same.
Now subtract:
[tex]\[
\frac{3}{6} - \frac{5}{6} = \frac{3 - 5}{6} = \frac{-2}{6} = -\frac{1}{3}
\][/tex]
Thus, the term you should 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 answer is [tex]\(-\frac{1}{3}x\)[/tex].
Let's compare the two expressions:
1. [tex]\(\frac{5}{6}x - 4\)[/tex]
2. [tex]\(\frac{1}{2}x - 4\)[/tex]
Notice that the constant term [tex]\(-4\)[/tex] is the same in both expressions. This means we only need to focus on the coefficients of [tex]\(x\)[/tex].
Now, let's find the difference between the coefficients of [tex]\(x\)[/tex] in the two expressions. The coefficient of [tex]\(x\)[/tex] in the first expression is [tex]\(\frac{5}{6}\)[/tex], and in the second expression, it is [tex]\(\frac{1}{2}\)[/tex].
To find what term should be added to [tex]\(\frac{5}{6}x\)[/tex] to make it [tex]\(\frac{1}{2}x\)[/tex], calculate:
[tex]\[
\frac{1}{2} - \frac{5}{6}
\][/tex]
To subtract these fractions, find a common denominator. The common denominator for 2 and 6 is 6:
- Convert [tex]\(\frac{1}{2}\)[/tex] to [tex]\(\frac{3}{6}\)[/tex] (because [tex]\(\frac{1 \times 3}{2 \times 3} = \frac{3}{6}\)[/tex]).
- [tex]\(\frac{5}{6}\)[/tex] stays the same.
Now subtract:
[tex]\[
\frac{3}{6} - \frac{5}{6} = \frac{3 - 5}{6} = \frac{-2}{6} = -\frac{1}{3}
\][/tex]
Thus, the term you should 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 answer is [tex]\(-\frac{1}{3}x\)[/tex].
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