Answer :
- First, calculate the product inside the absolute value: $6
cdot (-7) = -42$.
- Then, evaluate the absolute value: $|-42| = 42$.
- Multiply the absolute value by 2: $2
cdot 42 = 84$.
- Finally, add -10: $-10 + 84 = 74$. The final answer is $\boxed{74}$.
### Explanation
1. Understanding the expression
We are asked to evaluate the expression $-10+2|6
cdot(-7)|$. This involves order of operations, absolute value, and integer arithmetic.
2. Calculate inside absolute value
First, we need to evaluate the expression inside the absolute value, which is $6
cdot (-7)$. The product of a positive and a negative number is negative. $6
cdot 7 = 42$, so $6
cdot (-7) = -42$.
3. Evaluate the absolute value
Next, we take the absolute value of -42, which is the distance of -42 from 0. The absolute value of -42 is 42, so $|-42| = 42$.
4. Multiply by 2
Now, we multiply the absolute value by 2: $2
cdot 42 = 84$.
5. Add -10
Finally, we add -10 to the result: $-10 + 84 = 74$.
### Examples
Absolute value is used in many real-world scenarios, such as calculating distances or errors. For example, if you are measuring the distance between two points, you might get a negative value due to the direction you measured, but the actual distance is always positive, so you would use the absolute value. Similarly, in engineering, absolute value is used to calculate the magnitude of errors, regardless of whether the error is positive or negative.
cdot (-7) = -42$.
- Then, evaluate the absolute value: $|-42| = 42$.
- Multiply the absolute value by 2: $2
cdot 42 = 84$.
- Finally, add -10: $-10 + 84 = 74$. The final answer is $\boxed{74}$.
### Explanation
1. Understanding the expression
We are asked to evaluate the expression $-10+2|6
cdot(-7)|$. This involves order of operations, absolute value, and integer arithmetic.
2. Calculate inside absolute value
First, we need to evaluate the expression inside the absolute value, which is $6
cdot (-7)$. The product of a positive and a negative number is negative. $6
cdot 7 = 42$, so $6
cdot (-7) = -42$.
3. Evaluate the absolute value
Next, we take the absolute value of -42, which is the distance of -42 from 0. The absolute value of -42 is 42, so $|-42| = 42$.
4. Multiply by 2
Now, we multiply the absolute value by 2: $2
cdot 42 = 84$.
5. Add -10
Finally, we add -10 to the result: $-10 + 84 = 74$.
### Examples
Absolute value is used in many real-world scenarios, such as calculating distances or errors. For example, if you are measuring the distance between two points, you might get a negative value due to the direction you measured, but the actual distance is always positive, so you would use the absolute value. Similarly, in engineering, absolute value is used to calculate the magnitude of errors, regardless of whether the error is positive or negative.
