Math Problem Statement

4(w+7)-2(2w+1)

Solution

Let's simplify the given expression:
4(w+7)2(2w+1)4(w + 7) - 2(2w + 1)

Step 1: Apply the distributive property to both terms:

4(w+7)=4w+284(w + 7) = 4w + 28 2(2w+1)=4w2-2(2w + 1) = -4w - 2

Step 2: Combine the terms:

4w+284w24w + 28 - 4w - 2

Step 3: Simplify by combining like terms:

(4w4w)+(282)=0+26=26(4w - 4w) + (28 - 2) = 0 + 26 = 26

So, the simplified expression is:

26\boxed{26}

Would you like more details or have any questions about this process? Here are a few related questions to explore further:

  1. How do you apply the distributive property in algebraic expressions?
  2. What happens when we combine like terms in an expression?
  3. How do you solve an equation after simplifying an expression?
  4. What is the difference between simplifying and solving an algebraic equation?
  5. How do parentheses affect the simplification process in algebra?

Tip: When simplifying expressions, always look for like terms to combine and apply distributive properties first to make things easier!

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Math Problem Analysis

Mathematical Concepts

Algebra
Distributive Property
Simplifying Expressions

Formulas

Distributive Property: a(b + c) = ab + ac

Theorems

Distributive property of multiplication over addition

Suitable Grade Level

Grades 7-9