Answer :
To solve the problem, we want to determine 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].
1. Identify the two expressions:
- Expression 1: [tex]\(\frac{5}{6}x - 4\)[/tex]
- Expression 2: [tex]\(\frac{1}{2}x - 4\)[/tex]
2. Compare the expressions:
- Since both expressions have [tex]\(-4\)[/tex] as the constant term, we need to compare the terms involving [tex]\(x\)[/tex]. Specifically, we need to focus on the coefficients of [tex]\(x\)[/tex].
3. Find the difference in the coefficients of [tex]\(x\)[/tex]:
- Coefficient of [tex]\(x\)[/tex] in Expression 1: [tex]\(\frac{5}{6}\)[/tex]
- Coefficient of [tex]\(x\)[/tex] in Expression 2: [tex]\(\frac{1}{2}\)[/tex]
4. Calculate the difference between these coefficients:
- Find the difference: [tex]\(\frac{1}{2} - \frac{5}{6}\)[/tex]
5. Perform the subtraction:
- To subtract the fractions, first find a common denominator. The least common multiple of 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].
- Subtract: [tex]\(\frac{3}{6} - \frac{5}{6} = -\frac{2}{6} = -\frac{1}{3}\)[/tex]
6. Determine the term to add:
- The difference, [tex]\(-\frac{1}{3}\)[/tex], is the term that needs to be added to the coefficient of [tex]\(x\)[/tex] in Expression 1.
Therefore, 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].
The answer is [tex]\(-\frac{1}{3}x\)[/tex].
1. Identify the two expressions:
- Expression 1: [tex]\(\frac{5}{6}x - 4\)[/tex]
- Expression 2: [tex]\(\frac{1}{2}x - 4\)[/tex]
2. Compare the expressions:
- Since both expressions have [tex]\(-4\)[/tex] as the constant term, we need to compare the terms involving [tex]\(x\)[/tex]. Specifically, we need to focus on the coefficients of [tex]\(x\)[/tex].
3. Find the difference in the coefficients of [tex]\(x\)[/tex]:
- Coefficient of [tex]\(x\)[/tex] in Expression 1: [tex]\(\frac{5}{6}\)[/tex]
- Coefficient of [tex]\(x\)[/tex] in Expression 2: [tex]\(\frac{1}{2}\)[/tex]
4. Calculate the difference between these coefficients:
- Find the difference: [tex]\(\frac{1}{2} - \frac{5}{6}\)[/tex]
5. Perform the subtraction:
- To subtract the fractions, first find a common denominator. The least common multiple of 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].
- Subtract: [tex]\(\frac{3}{6} - \frac{5}{6} = -\frac{2}{6} = -\frac{1}{3}\)[/tex]
6. Determine the term to add:
- The difference, [tex]\(-\frac{1}{3}\)[/tex], is the term that needs to be added to the coefficient of [tex]\(x\)[/tex] in Expression 1.
Therefore, 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].
The answer is [tex]\(-\frac{1}{3}x\)[/tex].
