Math Problem Statement

Simplify the following expressions by combining like terms

8x + 7 - 8y + 6x - 8

What is the constant for the variable y after simplification

Solution

To simplify the expression 8x+78y+6x88x + 7 - 8y + 6x - 8, let's follow these steps:

Step 1: Group like terms

  1. Terms with xx: 8x8x and 6x6x
  2. Terms with yy: 8y-8y
  3. Constant terms: 77 and 8-8

Step 2: Combine like terms

  1. Combine xx terms: 8x+6x=14x8x + 6x = 14x
  2. The term with yy stays the same: 8y-8y
  3. Combine constant terms: 78=17 - 8 = -1

Final Expression

Combining all the simplified terms, we get: 14x8y114x - 8y - 1

Therefore, the constant for the variable yy after simplification is -8.


Would you like more details, or do you have any questions? Here are some related questions you might find interesting:

  1. What happens if a term doesn’t have a matching like term?
  2. How can you verify if your simplification is correct?
  3. What are the rules for adding and subtracting like terms?
  4. How can simplification help in solving equations?
  5. What is the significance of the coefficients in terms of variable dependency?
  6. How do you simplify expressions that include multiplication or division?
  7. How can you handle negative coefficients in simplification?
  8. Can you explain the distributive property in combining like terms?

Tip: Keep an eye on the signs of terms when combining like terms to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Combining Like Terms

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9