Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
Certainly! Let's verify the given equation step-by-step.
### Left Side of the Equation
First, we need to evaluate the left side of the equation:
[tex]\[ \frac{-3}{4} + \left[ \frac{1}{2} + \left( \frac{-1}{6} \right) \right] \][/tex]
1. Calculate inside the innermost brackets:
[tex]\[ \left( \frac{1}{2} + \left( \frac{-1}{6} \right) \right) = \frac{1}{2} - \frac{1}{6} \][/tex]
To subtract these fractions, we need a common denominator. The common denominator for 2 and 6 is 6.
[tex]\[ \frac{1}{2} = \frac{3}{6} \][/tex]
So,
[tex]\[ \frac{3}{6} - \frac{1}{6} = \frac{2}{6} = \frac{1}{3} \][/tex]
2. Add the result to \(\frac{-3}{4}\):
[tex]\[ \frac{-3}{4} + \frac{1}{3} \][/tex]
Again, find a common denominator for 4 and 3, which is 12.
[tex]\[ \frac{-3}{4} = \frac{-9}{12} \quad \text{and} \quad \frac{1}{3} = \frac{4}{12} \][/tex]
Thus,
[tex]\[ \frac{-9}{12} + \frac{4}{12} = \frac{-5}{12} \][/tex]
So, the left side of the equation simplifies to:
[tex]\[ \frac{-5}{12} \][/tex]
### Right Side of the Equation
Next, let's evaluate the right side of the equation:
[tex]\[ \left[ \frac{3}{4} + \frac{1}{2} \right] + \frac{-7}{6} \][/tex]
1. Calculate inside the brackets:
[tex]\[ \left( \frac{3}{4} + \frac{1}{2} \right) \][/tex]
Convert \(\frac{1}{2}\) to have a common denominator with \(\frac{3}{4}\), which is 4.
[tex]\[ \frac{1}{2} = \frac{2}{4} \][/tex]
So,
[tex]\[ \frac{3}{4} + \frac{2}{4} = \frac{5}{4} \][/tex]
2. Add the result to \(\frac{-7}{6}\):
[tex]\[ \frac{5}{4} + \frac{-7}{6} \][/tex]
Find a common denominator for 4 and 6, which is 12.
[tex]\[ \frac{5}{4} = \frac{15}{12} \quad \text{and} \quad \frac{-7}{6} = \frac{-14}{12} \][/tex]
Thus,
[tex]\[ \frac{15}{12} + \frac{-14}{12} = \frac{1}{12} \][/tex]
So, the right side of the equation simplifies to:
[tex]\[ \frac{1}{12} \][/tex]
### Compare Left and Right Sides
Finally, we compare the simplified expressions of both sides:
[tex]\[ \frac{-5}{12} \quad \text{(left side)} \quad \text{and} \quad \frac{1}{12} \quad \text{(right side)} \][/tex]
Clearly, \(\frac{-5}{12}\) does not equal \(\frac{1}{12}\).
### Conclusion
The two sides of the equation are not equal:
[tex]\[ \frac{-3}{4} + \left[ \frac{1}{2} + \left( \frac{-1}{6} \right) \right] \neq \left[ \frac{3}{4} + \frac{1}{2} \right] + \frac{-7}{6} \][/tex]
The verification shows that the left-hand side is [tex]\(\frac{-5}{12}\)[/tex] and the right-hand side is [tex]\(\frac{1}{12}\)[/tex], proving that the equation is false.
### Left Side of the Equation
First, we need to evaluate the left side of the equation:
[tex]\[ \frac{-3}{4} + \left[ \frac{1}{2} + \left( \frac{-1}{6} \right) \right] \][/tex]
1. Calculate inside the innermost brackets:
[tex]\[ \left( \frac{1}{2} + \left( \frac{-1}{6} \right) \right) = \frac{1}{2} - \frac{1}{6} \][/tex]
To subtract these fractions, we need a common denominator. The common denominator for 2 and 6 is 6.
[tex]\[ \frac{1}{2} = \frac{3}{6} \][/tex]
So,
[tex]\[ \frac{3}{6} - \frac{1}{6} = \frac{2}{6} = \frac{1}{3} \][/tex]
2. Add the result to \(\frac{-3}{4}\):
[tex]\[ \frac{-3}{4} + \frac{1}{3} \][/tex]
Again, find a common denominator for 4 and 3, which is 12.
[tex]\[ \frac{-3}{4} = \frac{-9}{12} \quad \text{and} \quad \frac{1}{3} = \frac{4}{12} \][/tex]
Thus,
[tex]\[ \frac{-9}{12} + \frac{4}{12} = \frac{-5}{12} \][/tex]
So, the left side of the equation simplifies to:
[tex]\[ \frac{-5}{12} \][/tex]
### Right Side of the Equation
Next, let's evaluate the right side of the equation:
[tex]\[ \left[ \frac{3}{4} + \frac{1}{2} \right] + \frac{-7}{6} \][/tex]
1. Calculate inside the brackets:
[tex]\[ \left( \frac{3}{4} + \frac{1}{2} \right) \][/tex]
Convert \(\frac{1}{2}\) to have a common denominator with \(\frac{3}{4}\), which is 4.
[tex]\[ \frac{1}{2} = \frac{2}{4} \][/tex]
So,
[tex]\[ \frac{3}{4} + \frac{2}{4} = \frac{5}{4} \][/tex]
2. Add the result to \(\frac{-7}{6}\):
[tex]\[ \frac{5}{4} + \frac{-7}{6} \][/tex]
Find a common denominator for 4 and 6, which is 12.
[tex]\[ \frac{5}{4} = \frac{15}{12} \quad \text{and} \quad \frac{-7}{6} = \frac{-14}{12} \][/tex]
Thus,
[tex]\[ \frac{15}{12} + \frac{-14}{12} = \frac{1}{12} \][/tex]
So, the right side of the equation simplifies to:
[tex]\[ \frac{1}{12} \][/tex]
### Compare Left and Right Sides
Finally, we compare the simplified expressions of both sides:
[tex]\[ \frac{-5}{12} \quad \text{(left side)} \quad \text{and} \quad \frac{1}{12} \quad \text{(right side)} \][/tex]
Clearly, \(\frac{-5}{12}\) does not equal \(\frac{1}{12}\).
### Conclusion
The two sides of the equation are not equal:
[tex]\[ \frac{-3}{4} + \left[ \frac{1}{2} + \left( \frac{-1}{6} \right) \right] \neq \left[ \frac{3}{4} + \frac{1}{2} \right] + \frac{-7}{6} \][/tex]
The verification shows that the left-hand side is [tex]\(\frac{-5}{12}\)[/tex] and the right-hand side is [tex]\(\frac{1}{12}\)[/tex], proving that the equation is false.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
