What is the value of $(+4)-(-3)$?
Answer (1)
Evaluate ( + 4 ) − ( − 3 ) : Adding the numbers gives 4 + 3 = 7 .
Find the missing integer: Solving − 14 + x = 20 yields x = 20 + 14 = 34 .
Find the integer 6 units left of 15: Subtracting gives 15 − 6 = 9 .
Determine the value of 5 units right and 4 units left to 0: Calculating gives 0 + 5 − 4 = 1 . The final answer to the first question is 7 .
Explanation
Introduction We are given a series of math problems to solve. Let's address them one by one.
Calculating (+4)-(-3) First, we need to evaluate the expression ( + 4 ) − ( − 3 ) . Subtracting a negative number is the same as adding its positive counterpart. Therefore, ( + 4 ) − ( − 3 ) = 4 + 3 = 7 .
Finding the missing integer Next, we are told that the sum of two integers is +20, and one of the integers is -14. We need to find the other integer. Let's call the unknown integer x . We have the equation − 14 + x = 20 . To solve for x , we add 14 to both sides of the equation: x = 20 + 14 = 34 .
Finding the integer 6 units left of 15 We need to find the integer that lies 6 units to the left of 15 on the number line. This means we need to subtract 6 from 15: 15 − 6 = 9 .
5 units right and 4 units left to 0 We need to find the value of 5 units right and 4 units left to 0 on the number line. This is equivalent to 0 + 5 − 4 = 1 .
4 units right and 5 units left to 0 We need to find the value of 4 units right and 5 units left to 0 on the number line. This is equivalent to 0 + 4 − 5 = − 1 .
5 units right and 6 units left to 3 We need to find the value of 5 units right and 6 units left to 3 on the number line. This is equivalent to 3 + 5 − 6 = 2 .
6 units right and 3 units left to 3 We need to find the value of 6 units right and 3 units left to 3 on the number line. This is equivalent to 3 + 6 − 3 = 6 .
Listing elements of sets We are given sets of integers. Let's list the elements of each set:
A = { integers between +3 and -3 } = { − 2 , − 1 , 0 , 1 , 2 }
B = { integers between -2 and +2 } = { − 1 , 0 , 1 }
C = { integers between -4 and +3 } = { − 3 , − 2 , − 1 , 0 , 1 , 2 }
D = { integers between +5 and +8 } = { 6 , 7 }
Final Answers The value of ( + 4 ) − ( − 3 ) is 7. The sum of two integers is +20 and one of the integer is -14, the other integer is 34. The integer that lies 6 units left to the 15 is 9. On the number line from -10 to 10, 5 units right and 4 units left to 0 is 1. On the number line from -10 to 10, 4 units right and 5 units left to 0 is -1. On the number line from -10 to 10, 5 units right and 6 units left to 3 is 2. On the number line from -10 to 10, 6 units right and 3 units left to 3 is 6. A = { − 2 , − 1 , 0 , 1 , 2 } B = { − 1 , 0 , 1 } C = { − 3 , − 2 , − 1 , 0 , 1 , 2 } D = { 6 , 7 }
Examples
These math problems are fundamental in various real-life scenarios. For instance, calculating temperature changes involves subtracting negative numbers, similar to (+4)-(-3). Balancing a checkbook or tracking expenses often requires finding a missing value when you know the total and one of the amounts, just like finding the missing integer. Determining distances and positions, such as finding a location relative to a starting point, uses number line concepts. Understanding sets of numbers is crucial in data analysis and organization, helping to categorize and manage information effectively.
