Math Problem Statement

Simplify the following algebraic expressions: 1. x + 4 2. x - 4 3. (3x + 2) + (3x - 4) 4. (2x + 3) + (5x - 8) 5. (2x + 5) - (4x + 3) 6. 10x - 5x 7. 2x - 3x 8. 5x + 6y - 5x 9. 6x - 5x 10. 5x - 5x

Solution

The image contains several algebraic expressions, likely asking to simplify or solve them. I will extract the expressions and guide you through solving them.

Here are the expressions from the image:

  1. x+4x + 4
  2. x4x - 4
  3. (3x+2)+(3x4)(3x + 2) + (3x - 4)
  4. (2x+3)+(5x8)(2x + 3) + (5x - 8)
  5. (2x+5)(4x+3)(2x + 5) - (4x + 3)
  6. 10x5x10x - 5x
  7. 2x3x2x - 3x
  8. 5x+6y5x5x + 6y - 5x
  9. 6x5x6x - 5x
  10. 5x5x5x - 5x

Now, let's simplify these expressions one by one:

  1. x+4x + 4 (already simplified)
  2. x4x - 4 (already simplified)
  3. (3x+2)+(3x4)=3x+2+3x4=6x2(3x + 2) + (3x - 4) = 3x + 2 + 3x - 4 = 6x - 2
  4. (2x+3)+(5x8)=2x+3+5x8=7x5(2x + 3) + (5x - 8) = 2x + 3 + 5x - 8 = 7x - 5
  5. (2x+5)(4x+3)=2x+54x3=2x+2(2x + 5) - (4x + 3) = 2x + 5 - 4x - 3 = -2x + 2
  6. 10x5x=5x10x - 5x = 5x
  7. 2x3x=x2x - 3x = -x
  8. 5x+6y5x=6y5x + 6y - 5x = 6y
  9. 6x5x=x6x - 5x = x
  10. 5x5x=05x - 5x = 0

Would you like more details on any of these steps? Here are five related questions to further practice this topic:

  1. How do you simplify expressions involving both like and unlike terms?
  2. What is the process of combining like terms in an algebraic expression?
  3. Can you explain how to simplify the expression (x2+3x)+(2x2x)(x^2 + 3x) + (2x^2 - x)?
  4. What happens when you subtract a variable term from itself, such as 5x5x5x - 5x?
  5. How would you simplify expressions that involve both positive and negative coefficients?

Tip: Always combine like terms by focusing on their coefficients, ensuring the same variable with the same power is grouped together.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Expressions
Combining Like Terms

Formulas

Combining like terms: ax + bx = (a+b)x

Theorems

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Suitable Grade Level

Grades 7-9