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Answer :
Sure! Let's solve the problem step by step.
We want to make the expressions [tex]\(\frac{5}{6}x - 4\)[/tex] and [tex]\(\frac{1}{2}x - 4\)[/tex] equivalent. To do this, we need to find a term that, when added to [tex]\(\frac{5}{6}x - 4\)[/tex], results in [tex]\(\frac{1}{2}x - 4\)[/tex].
We can focus on the parts of the expressions that contain [tex]\(x\)[/tex], since the [tex]\(-4\)[/tex] in both expressions is already equal.
1. Identify the Expressions to Compare:
- We are comparing the terms with [tex]\(x\)[/tex]: [tex]\(\frac{5}{6}x\)[/tex] and [tex]\(\frac{1}{2}x\)[/tex].
2. Set Up the Equation:
- To find the term we need to add, we set up the equation:
[tex]\[
\frac{5}{6}x + \text{(term)} = \frac{1}{2}x
\][/tex]
3. Find the Needed Term:
- We solve for the term by subtracting [tex]\(\frac{5}{6}x\)[/tex] from both sides:
[tex]\[
\text{(term)} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Subtract the Fractions:
- To subtract these fractions, we need a common denominator. The least common denominator of 2 and 6 is 6:
[tex]\[
\frac{1}{2} = \frac{3}{6}
\][/tex]
[tex]\[
\frac{1}{2}x - \frac{5}{6}x = \frac{3}{6}x - \frac{5}{6}x
\][/tex]
5. Simplify the Equation:
- Subtract the fractions:
[tex]\[
\frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
6. Reduce the Fraction:
- Simplify [tex]\(-\frac{2}{6}\)[/tex] to [tex]\(-\frac{1}{3}\)[/tex]:
[tex]\[
-\frac{2}{6}x = -\frac{1}{3}x
\][/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 correct answer is [tex]\(-\frac{1}{3}x\)[/tex].
We want to make the expressions [tex]\(\frac{5}{6}x - 4\)[/tex] and [tex]\(\frac{1}{2}x - 4\)[/tex] equivalent. To do this, we need to find a term that, when added to [tex]\(\frac{5}{6}x - 4\)[/tex], results in [tex]\(\frac{1}{2}x - 4\)[/tex].
We can focus on the parts of the expressions that contain [tex]\(x\)[/tex], since the [tex]\(-4\)[/tex] in both expressions is already equal.
1. Identify the Expressions to Compare:
- We are comparing the terms with [tex]\(x\)[/tex]: [tex]\(\frac{5}{6}x\)[/tex] and [tex]\(\frac{1}{2}x\)[/tex].
2. Set Up the Equation:
- To find the term we need to add, we set up the equation:
[tex]\[
\frac{5}{6}x + \text{(term)} = \frac{1}{2}x
\][/tex]
3. Find the Needed Term:
- We solve for the term by subtracting [tex]\(\frac{5}{6}x\)[/tex] from both sides:
[tex]\[
\text{(term)} = \frac{1}{2}x - \frac{5}{6}x
\][/tex]
4. Subtract the Fractions:
- To subtract these fractions, we need a common denominator. The least common denominator of 2 and 6 is 6:
[tex]\[
\frac{1}{2} = \frac{3}{6}
\][/tex]
[tex]\[
\frac{1}{2}x - \frac{5}{6}x = \frac{3}{6}x - \frac{5}{6}x
\][/tex]
5. Simplify the Equation:
- Subtract the fractions:
[tex]\[
\frac{3}{6}x - \frac{5}{6}x = -\frac{2}{6}x
\][/tex]
6. Reduce the Fraction:
- Simplify [tex]\(-\frac{2}{6}\)[/tex] to [tex]\(-\frac{1}{3}\)[/tex]:
[tex]\[
-\frac{2}{6}x = -\frac{1}{3}x
\][/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 correct answer is [tex]\(-\frac{1}{3}x\)[/tex].
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