Math Problem Statement

Simplify the expression 12x - 2(9 - x)

Solution

The expression in the image is:

12x2(9x)12x - 2(9 - x)

Let's simplify it step by step:

  1. Distribute the 2-2 across the terms inside the parentheses: 12x2(9)+2(x)12x - 2(9) + 2(x) This becomes: 12x18+2x12x - 18 + 2x

  2. Combine like terms: (12x+2x)18=14x18(12x + 2x) - 18 = 14x - 18

So, the simplified expression is:

14x1814x - 18

Let me know if you'd like further details!

Here are five related questions you might want to explore:

  1. How would you solve the equation 14x18=014x - 18 = 0?
  2. What happens if you add a constant to both sides of the equation?
  3. How does the distributive property work in similar problems?
  4. Can you solve 12x2(9x)=2012x - 2(9 - x) = 20?
  5. How would the expression change if the numbers were different, such as 12x3(9x)12x - 3(9 - x)?

Tip: Always distribute negative signs carefully when simplifying expressions, as they often cause errors.

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Math Problem Analysis

Mathematical Concepts

Algebra
Distributive Property

Formulas

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

Theorems

Distributive Property

Suitable Grade Level

Grades 6-8