Math Problem Statement

Simplify the algebraic expression: 2(x + 9) - 7x + 4.

Solution

The equation in the image is:

2(x+9)7x+42(x + 9) - 7x + 4

Let’s solve and simplify this step by step.

Step 1: Distribute the 2 across the terms inside the parentheses.

2(x+9)=2x+182(x + 9) = 2x + 18

So the expression becomes: 2x+187x+42x + 18 - 7x + 4

Step 2: Combine like terms.

  • Combine 2x2x and 7x-7x: 2x7x=5x2x - 7x = -5x
  • Combine 1818 and 44: 18+4=2218 + 4 = 22

Now, the expression simplifies to: 5x+22-5x + 22

Final Answer:

The simplified form of the expression is: 5x+22-5x + 22

Would you like more details, or do you have any other questions?

Here are 5 related questions:

  1. How do you solve equations with parentheses and distribution?
  2. How do you combine like terms in algebraic expressions?
  3. What are the steps to factor a linear expression like 5x+22-5x + 22?
  4. Can this expression be set equal to zero and solved for xx?
  5. How does the order of operations affect simplifying algebraic expressions?

Tip: Always distribute before combining like terms when simplifying expressions involving parentheses.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification
Distribution
Combining Like Terms

Formulas

Distribution: a(b + c) = ab + ac

Theorems

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Suitable Grade Level

Grades 6-8