Answer :
To solve the problem of finding what term should be added to [tex]\(\frac{5}{6}x - 4\)[/tex] to make it equivalent to [tex]\(\frac{1}{2}x - 4\)[/tex], we need to focus on the [tex]\(x\)[/tex] terms in each expression.
1. We start with the expression [tex]\(\frac{5}{6}x - 4\)[/tex] and we want it to be equal to [tex]\(\frac{1}{2}x - 4\)[/tex].
2. Since the constants (-4 in both cases) are already equal, we only need to adjust the [tex]\(x\)[/tex] term.
3. Set up the equation based on the [tex]\(x\)[/tex] terms:
[tex]\[
\frac{5}{6}x + A = \frac{1}{2}x
\][/tex]
Here, [tex]\(A\)[/tex] is the term we need to add to [tex]\(\frac{5}{6}x\)[/tex].
4. To find [tex]\(A\)[/tex], subtract [tex]\(\frac{5}{6}x\)[/tex] from both sides of the equation:
[tex]\[
A = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
5. Find a common denominator to subtract the fractions. The common denominator between 2 and 6 is 6.
Convert [tex]\(\frac{1}{2}x\)[/tex] into [tex]\(\frac{3}{6}x\)[/tex]:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
6. Now, subtract the fractions:
[tex]\[
A = \frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
7. Simplify [tex]\(-\frac{2}{6}x\)[/tex] to [tex]\(-\frac{1}{3}x\)[/tex].
So, the term you can 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].
1. We start with the expression [tex]\(\frac{5}{6}x - 4\)[/tex] and we want it to be equal to [tex]\(\frac{1}{2}x - 4\)[/tex].
2. Since the constants (-4 in both cases) are already equal, we only need to adjust the [tex]\(x\)[/tex] term.
3. Set up the equation based on the [tex]\(x\)[/tex] terms:
[tex]\[
\frac{5}{6}x + A = \frac{1}{2}x
\][/tex]
Here, [tex]\(A\)[/tex] is the term we need to add to [tex]\(\frac{5}{6}x\)[/tex].
4. To find [tex]\(A\)[/tex], subtract [tex]\(\frac{5}{6}x\)[/tex] from both sides of the equation:
[tex]\[
A = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
5. Find a common denominator to subtract the fractions. The common denominator between 2 and 6 is 6.
Convert [tex]\(\frac{1}{2}x\)[/tex] into [tex]\(\frac{3}{6}x\)[/tex]:
[tex]\[
\frac{1}{2}x = \frac{3}{6}x
\][/tex]
6. Now, subtract the fractions:
[tex]\[
A = \frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
7. Simplify [tex]\(-\frac{2}{6}x\)[/tex] to [tex]\(-\frac{1}{3}x\)[/tex].
So, the term you can 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].
