Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
To verify the equation
[tex]\[ \frac{-3}{4}+\left(\frac{1}{2}+\left(\frac{-7}{6}\right)\right)=\left(\frac{3}{4}+\frac{1}{2}\right)+\frac{-7}{6}, \][/tex]
we will evaluate each side of the equation separately and then compare the results.
First, let's evaluate the left-hand side (LHS):
[tex]\[ \text{LHS} = \frac{-3}{4} + \left(\frac{1}{2} + \frac{-7}{6}\right) \][/tex]
Step 1: Calculate the value inside the parentheses:
[tex]\[ \frac{1}{2} + \frac{-7}{6} \][/tex]
To add these fractions, we need a common denominator. The least common denominator of 2 and 6 is 6, so we convert each fraction:
[tex]\[ \frac{1}{2} = \frac{3}{6}, \quad \frac{-7}{6} = \frac{-7}{6} \][/tex]
Now, we add the fractions:
[tex]\[ \frac{3}{6} + \frac{-7}{6} = \frac{3 - 7}{6} = \frac{-4}{6} = \frac{-2}{3} \][/tex]
Step 2: Now, add this result to \(\frac{-3}{4}\):
[tex]\[ \frac{-3}{4} + \frac{-2}{3} \][/tex]
Again, we need a common denominator to add these fractions. The least common denominator of 4 and 3 is 12, so we convert each fraction:
[tex]\[ \frac{-3}{4} = \frac{-9}{12}, \quad \frac{-2}{3} = \frac{-8}{12} \][/tex]
Now, we add the fractions:
[tex]\[ \frac{-9}{12} + \frac{-8}{12} = \frac{-9 - 8}{12} = \frac{-17}{12} \][/tex]
So, the left-hand side simplifies to:
[tex]\[ \text{LHS} = \frac{-17}{12} = -1.4166666666666667 \][/tex]
Next, let's evaluate the right-hand side (RHS):
[tex]\[ \text{RHS} = \left(\frac{3}{4} + \frac{1}{2}\right) + \frac{-7}{6} \][/tex]
Step 1: Calculate the value inside the parentheses:
[tex]\[ \frac{3}{4} + \frac{1}{2} \][/tex]
Again, we need a common denominator. The least common denominator of 4 and 2 is 4, so we convert each fraction:
[tex]\[ \frac{3}{4} = \frac{3}{4}, \quad \frac{1}{2} = \frac{2}{4} \][/tex]
Now, we add the fractions:
[tex]\[ \frac{3}{4} + \frac{2}{4} = \frac{3 + 2}{4} = \frac{5}{4} \][/tex]
Step 2: Now, add this result to \(\frac{-7}{6}\):
[tex]\[ \frac{5}{4} + \frac{-7}{6} \][/tex]
We need a common denominator to add these fractions. The least common denominator of 4 and 6 is 12, so we convert each fraction:
[tex]\[ \frac{5}{4} = \frac{15}{12}, \quad \frac{-7}{6} = \frac{-14}{12} \][/tex]
Now, we add the fractions:
[tex]\[ \frac{15}{12} + \frac{-14}{12} = \frac{15 - 14}{12} = \frac{1}{12} \][/tex]
So, the right-hand side simplifies to:
[tex]\[ \text{RHS} = \frac{1}{12} = 0.08333333333333326 \][/tex]
Finally, we compare the two sides. The left-hand side is \(-1.4166666666666667\) and the right-hand side is \(0.08333333333333326\).
Since \(\text{LHS} \ne \text{RHS}\), the original equation
[tex]\[ \frac{-3}{4}+\left(\frac{1}{2}+\left(\frac{-7}{6}\right)\right)\neq\left(\frac{3}{4}+\frac{1}{2}\right)+\frac{-7}{6} \][/tex]
is not valid.
[tex]\[ \frac{-3}{4}+\left(\frac{1}{2}+\left(\frac{-7}{6}\right)\right)=\left(\frac{3}{4}+\frac{1}{2}\right)+\frac{-7}{6}, \][/tex]
we will evaluate each side of the equation separately and then compare the results.
First, let's evaluate the left-hand side (LHS):
[tex]\[ \text{LHS} = \frac{-3}{4} + \left(\frac{1}{2} + \frac{-7}{6}\right) \][/tex]
Step 1: Calculate the value inside the parentheses:
[tex]\[ \frac{1}{2} + \frac{-7}{6} \][/tex]
To add these fractions, we need a common denominator. The least common denominator of 2 and 6 is 6, so we convert each fraction:
[tex]\[ \frac{1}{2} = \frac{3}{6}, \quad \frac{-7}{6} = \frac{-7}{6} \][/tex]
Now, we add the fractions:
[tex]\[ \frac{3}{6} + \frac{-7}{6} = \frac{3 - 7}{6} = \frac{-4}{6} = \frac{-2}{3} \][/tex]
Step 2: Now, add this result to \(\frac{-3}{4}\):
[tex]\[ \frac{-3}{4} + \frac{-2}{3} \][/tex]
Again, we need a common denominator to add these fractions. The least common denominator of 4 and 3 is 12, so we convert each fraction:
[tex]\[ \frac{-3}{4} = \frac{-9}{12}, \quad \frac{-2}{3} = \frac{-8}{12} \][/tex]
Now, we add the fractions:
[tex]\[ \frac{-9}{12} + \frac{-8}{12} = \frac{-9 - 8}{12} = \frac{-17}{12} \][/tex]
So, the left-hand side simplifies to:
[tex]\[ \text{LHS} = \frac{-17}{12} = -1.4166666666666667 \][/tex]
Next, let's evaluate the right-hand side (RHS):
[tex]\[ \text{RHS} = \left(\frac{3}{4} + \frac{1}{2}\right) + \frac{-7}{6} \][/tex]
Step 1: Calculate the value inside the parentheses:
[tex]\[ \frac{3}{4} + \frac{1}{2} \][/tex]
Again, we need a common denominator. The least common denominator of 4 and 2 is 4, so we convert each fraction:
[tex]\[ \frac{3}{4} = \frac{3}{4}, \quad \frac{1}{2} = \frac{2}{4} \][/tex]
Now, we add the fractions:
[tex]\[ \frac{3}{4} + \frac{2}{4} = \frac{3 + 2}{4} = \frac{5}{4} \][/tex]
Step 2: Now, add this result to \(\frac{-7}{6}\):
[tex]\[ \frac{5}{4} + \frac{-7}{6} \][/tex]
We need a common denominator to add these fractions. The least common denominator of 4 and 6 is 12, so we convert each fraction:
[tex]\[ \frac{5}{4} = \frac{15}{12}, \quad \frac{-7}{6} = \frac{-14}{12} \][/tex]
Now, we add the fractions:
[tex]\[ \frac{15}{12} + \frac{-14}{12} = \frac{15 - 14}{12} = \frac{1}{12} \][/tex]
So, the right-hand side simplifies to:
[tex]\[ \text{RHS} = \frac{1}{12} = 0.08333333333333326 \][/tex]
Finally, we compare the two sides. The left-hand side is \(-1.4166666666666667\) and the right-hand side is \(0.08333333333333326\).
Since \(\text{LHS} \ne \text{RHS}\), the original equation
[tex]\[ \frac{-3}{4}+\left(\frac{1}{2}+\left(\frac{-7}{6}\right)\right)\neq\left(\frac{3}{4}+\frac{1}{2}\right)+\frac{-7}{6} \][/tex]
is not valid.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
