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Let's work through the exercises step by step:

### Simplify:

**14. (+3) + (−14)**  
\( 3 + (-14) = 3 - 14 = -11 \)

**15. (−3) + (−14)**  
\( -3 + (-14) = -17 \)

**16. (−5) + (+4) + (−3) + (+8)**  
\( -5 + 4 - 3 + 8 = 4 + 8 - 5 - 3 = 12 - 8 = 4 \)

**17. (−3) + (+2) + (−2) + |−2|**  
First, calculate the absolute value \( |-2| = 2 \).  
\( -3 + 2 - 2 + 2 = -3 + 2 = -1 - 2 + 2 = -1 \)

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### Use parentheses to enclose each number and its sign. Then insert plus signs between the parentheses and add to get a sum:

**18. −2 + 11 − 4 + 3 − 8**  
Add parentheses:  
\( (-2) + (+11) + (-4) + (+3) + (-8) \)  
Now sum:  
\( -2 + 11 - 4 + 3 - 8 = 11 + 3 - 2 - 4 - 8 = 14 - 14 = 0 \)

**19. −5 − 11 + 20 − 14 + 5**  
Add parentheses:  
\( (-5) + (-11) + (+20) + (-14) + (+5) \)  
Now sum:  
\( -5 - 11 + 20 - 14 + 5 = -16 + 20 - 14 + 5 = 4 - 14 + 5 = -10 + 5 = -5 \)

**20. −4 − 3 + 2 − 4 − 3 − 8**  
Add parentheses:  
\( (-4) + (-3) + (+2) + (-4) + (-3) + (-8) \)  
Now sum:  
\( -4 - 3 + 2 - 4 - 3 - 8 = -7 + 2 - 4 - 3 - 8 = -5 - 4 - 3 - 8 = -20 \)

**21. 7 − 3 + 2 − 11 + 4 − 5 + 3**  
Add parentheses:  
\( (+7) + (-3) + (+2) + (-11) + (+4) + (-5) + (+3) \)  
Now sum:  
\( 7 - 3 + 2 - 11 + 4 - 5 + 3 = 4 + 2 - 11 + 4 - 5 + 3 = 6 - 11 + 4 - 5 + 3 = -5 + 4 - 5 + 3 = -1 + 3 = 2 \)

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### Use parentheses to enclose each number or expression and its sign. Then insert plus signs between the parentheses. Then add to get a sum:

**22. −7 + (−8) + 3**  
Add parentheses:  
\( (-7) + (-8) + (+3) \)  
Now sum:  
\( -7 - 8 + 3 = -15 + 3 = -12 \)

**23. −7 + (−3) + 4 − 3 + (−2)**  
Add parentheses:  
\( (-7) + (-3) + (+4) + (-3) + (-2) \)  
Now sum:  
\( -7 - 3 + 4 - 3 - 2 = -10 + 4 - 3 - 2 = -6 - 3 - 2 = -11 \)

**24. −4 − 2 + (+8) + |−5|**  
First, calculate the absolute value \( |-5| = 5 \).  
Add parentheses:  
\( (-4) + (-2) + (+8) + (+5) \)  
Now sum:  
\( -4 - 2 + 8 + 5 = -6 + 8 + 5 = 2 + 5 = 7 \)

**25. +|−2 − 3| − 4 + (−8)**  
First, simplify the absolute value \( |-2 - 3| = |-5| = 5 \).  
Now add parentheses:  
\( (+5) + (-4) + (-8) \)  
Now sum:  
\( 5 - 4 - 8 = 1 - 8 = -7 \)

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Would you like any details or further clarification? 

### Related questions:
1. How do you calculate absolute values in an expression?
2. What happens when you add two negative numbers together?
3. How do parentheses affect the order of operations in an expression?
4. How can you simplify complex expressions with mixed positive and negative terms?
5. What is the difference between subtracting a number and adding a negative number?

### Tip:
Always start solving expressions by calculating values inside absolute value symbols and parentheses first to avoid confusion.

Simplify the following mathematical expressions, including adding integers and absolute values, and insert parentheses where necessary to solve.

Learn how to simplify expressions involving integer addition, subtraction, and absolute values. This example includes detailed steps for using parentheses to solve the expressions. Suitable for middle school students in Grades 6-8.

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