https://file.aiquickdraw.com/mathbot/file/1725586448524aqmgyrsp.jpg

The image contains several algebraic expressions that need to be simplified. Here is a breakdown of each problem from the image:

1) **Expression 1:**  
\( 4x + 5x + 7 + x + 2 \)

2) **Expression 2:**  
\( 2n + 3 - 5n + 6 \)

3) **Expression 3:**  
\( -9b + 2n - 4 + 2b \)

4) **Expression 4:**  
\( -7g + 3 - 8 - 3g + 7h \)

5) **Expression 5:**  
\( -8 + 2d - 7 - 5d + 12 \)

6) **Expression 6:**  
\( 5b + 7 - 3b - 4 \)

I'll now simplify each of these expressions step by step:

### Simplified Expressions:

1) **Expression 1: \(4x + 5x + 7 + x + 2\)**  
Combine like terms (all terms with \(x\) and all constants):
\[
4x + 5x + x = 10x, \quad 7 + 2 = 9
\]  
Simplified expression:  
\[
10x + 9
\]

2) **Expression 2: \(2n + 3 - 5n + 6\)**  
Combine like terms (all terms with \(n\) and all constants):
\[
2n - 5n = -3n, \quad 3 + 6 = 9
\]  
Simplified expression:  
\[
-3n + 9
\]

3) **Expression 3: \(-9b + 2n - 4 + 2b\)**  
Combine like terms (all terms with \(b\) and \(n\), and constants):
\[
-9b + 2b = -7b, \quad 2n = 2n, \quad -4 = -4
\]  
Simplified expression:  
\[
-7b + 2n - 4
\]

4) **Expression 4: \(-7g + 3 - 8 - 3g + 7h\)**  
Combine like terms (all terms with \(g\), \(h\), and constants):
\[
-7g - 3g = -10g, \quad 7h = 7h, \quad 3 - 8 = -5
\]  
Simplified expression:  
\[
-10g + 7h - 5
\]

5) **Expression 5: \(-8 + 2d - 7 - 5d + 12\)**  
Combine like terms (all terms with \(d\) and constants):
\[
2d - 5d = -3d, \quad -8 - 7 + 12 = -3
\]  
Simplified expression:  
\[
-3d - 3
\]

6) **Expression 6: \(5b + 7 - 3b - 4\)**  
Combine like terms (all terms with \(b\) and constants):
\[
5b - 3b = 2b, \quad 7 - 4 = 3
\]  
Simplified expression:  
\[
2b + 3
\]

### Summary of Simplified Expressions:

1) \(10x + 9\)  
2) \(-3n + 9\)  
3) \(-7b + 2n - 4\)  
4) \(-10g + 7h - 5\)  
5) \(-3d - 3\)  
6) \(2b + 3\)  

Would you like to see further details or explanations for any of these steps? 

Here are some questions to explore further:
1. How do we handle negative coefficients when simplifying expressions?
2. What are like terms, and why do we combine them?
3. How can you check if your simplified expression is correct?
4. How would these expressions change if there were additional variables involved?
5. What methods can you use to solve equations after simplifying expressions?

**Tip:** Always double-check your work by substituting numbers for the variables to ensure both the original and simplified expressions give the same result.

Simplify the following expressions: 1) 4x + 5x + 7 + x + 2  2) 2n + 3 - 5n + 6  3) -9b + 2n - 4 + 2b  4) -7g + 3 - 8 - 3g + 7h  5) -8 + 2d - 7 - 5d + 12  6) 5b + 7 - 3b - 4

Learn how to simplify algebraic expressions such as 4x + 5x + 7 + x + 2 with step-by-step guidance on combining like terms. Ideal for students in Grades 7-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation