Math Problem Statement
Simplify the following expressions:
(10) -7a - (-2a + 4b)
(11) 3a - (b + 5a)
(12) (3a + 2) - (-a + 5)
Solution
I see the three problems presented in the image. Let's go through them one by one.
Problem (10):
- Distribute the negative sign through the parentheses:
- Combine like terms:
Thus, the simplified expression is:
Problem (11):
- Distribute the negative sign through the parentheses:
- Combine like terms:
Thus, the simplified expression is:
Problem (12):
- Distribute the negative sign through the parentheses:
- Combine like terms:
Thus, the simplified expression is:
Would you like further clarification on any of these steps?
Here are 5 related questions to deepen your understanding:
- How do you handle distribution when there is a negative sign outside parentheses?
- What is the importance of combining like terms in algebraic expressions?
- How can you identify like terms quickly in complex expressions?
- What would happen if you incorrectly distribute a negative sign in an equation?
- Can these simplified expressions be factored further, and why or why not?
Tip: Always pay close attention to signs when distributing; small mistakes with negatives can lead to incorrect solutions!
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Math Problem Analysis
Mathematical Concepts
Algebra
Simplifying Expressions
Distribution
Combining Like Terms
Formulas
a - (-b) = a + b
Distributive Property: a(b + c) = ab + ac
Theorems
Distributive Property
Associative Property of Addition
Suitable Grade Level
Grades 7-9