At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
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.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
