Using appropriate properties, find: (i) Verify that -(-y) = x for x = -11/15. (ii) Find the multiplicative inverse of -13. (iii) Write the additive inverse of each of the following... Using appropriate properties, find: (i) Verify that -(-y) = x for x = -11/15. (ii) Find the multiplicative inverse of -13. (iii) Write the additive inverse of each of the following: 2, -5, 5/6.
Understand the Problem
The question includes several mathematical problems involving verification of properties, finding values for equations, and determining the additive inverse of numbers. It is asking for solutions based on different mathematical principles.
Answer
1. $x = \frac{11}{15}$. 2. Result: $-6$. 3. Total: $12$. 4. Additive inverses: $5$ (for $-5$) and $6$ (for $-6$).
Answer for screen readers
- $x = \frac{11}{15}$ is verified.
- The result of the expression is $-6$.
- The total after substitution is $12$.
- The additive inverses are:
- Additive inverse of $-5$ is $5$.
- Additive inverse of $-6$ is $6$.
Steps to Solve
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Evaluate the first expression
Calculate $-\left( -\frac{11}{15} \right)$ to verify if it equals $x$.
Since $-\left( -\frac{11}{15} \right) = \frac{11}{15}$, this means $x = \frac{11}{15}$ is verified. -
Evaluate the second expression
Calculate the expression $3 - 2 \times 3 - 3$. First, perform the multiplication:
$$2 \times 3 = 6$$
Then rewrite the expression:
$$3 - 6 - 3$$
Now perform the addition/subtraction from left to right:
$$3 - 6 = -3$$
Then,
$$-3 - 3 = -6$$ -
Evaluate the third expression
Calculate the expression $5 + 2 - 5 - x - 1$. Substitute the value from the previous step:
$$5 + 2 - 5 - (-6) - 1$$
Now simplify:
$$7 - (-6) - 1$$
This results in:
$$7 + 6 - 1 = 12$$ -
Determine the additive inverse
Identify the additive inverse of the following:
- For $-5$, the additive inverse is $5$.
- For $-6$, the additive inverse is $6$.
- $x = \frac{11}{15}$ is verified.
- The result of the expression is $-6$.
- The total after substitution is $12$.
- The additive inverses are:
- Additive inverse of $-5$ is $5$.
- Additive inverse of $-6$ is $6$.
More Information
The verification shows the property of double negation in mathematics, where $-\left(-a\right) = a$. Calculating the additive inverse is a fundamental concept in algebra, aiding in understanding how numbers interact.
Tips
- Forgetting the order of operations can lead to incorrect answers; remember to perform multiplication before addition or subtraction.
- Misunderstanding the additive inverse; it is the number that when added to the original number gives zero.
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