Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
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.
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
