Math Problem Statement

Expand and simplify 2(x + 7) + 3(x + 1)

Solution

The expression in the image is:

2(x+7)+3(x+1)2(x + 7) + 3(x + 1)

Let's expand and simplify it step by step:

  1. Distribute the numbers outside the parentheses: 2(x+7)=2x+142(x + 7) = 2x + 14 3(x+1)=3x+33(x + 1) = 3x + 3

  2. Now, add the two expanded expressions together: 2x+14+3x+32x + 14 + 3x + 3

  3. Combine the like terms (the xx-terms and the constants): (2x+3x)+(14+3)=5x+17(2x + 3x) + (14 + 3) = 5x + 17

So, the simplified expression is:

5x+175x + 17

Would you like further explanation or details?

Here are 5 related questions to consider:

  1. How do you solve an equation involving parentheses and multiple terms?
  2. What is the distributive property, and how does it apply here?
  3. How would the process change if there were negative signs in the parentheses?
  4. Can this method be used to simplify more complex polynomials?
  5. How can factoring help reverse the process of expanding?

Tip: Always look for like terms after distributing to simplify your expressions efficiently!

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification
Distributive Property

Formulas

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

Theorems

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Suitable Grade Level

Grades 6-8