Understand the Problem
The text provides definitions and explanations of several mathematical concepts related to exponents, combining like terms, the distributive property, translating words into expressions, equivalent expressions, and evaluating expressions. It serves as a guide for understanding these concepts.
Answer
The final simplified expression is $7x + 6$.
Answer for screen readers
The final simplified expression is $7x + 6$.
Steps to Solve
-
Identify Key Concepts From the Text
First, identify the key concepts related to exponents, like terms, the distributive property, translating words into expressions, equivalent expressions, and evaluating expressions. These concepts will guide you in solving mathematical expressions and equations. -
Define Each Mathematical Concept
Next, for better understanding, define each of the key concepts.
- Exponents: Represents repeated multiplication of a number by itself. For example, $a^n = a \times a \times \cdots \times a$ (n times).
- Combining Like Terms: This involves simplifying expressions by adding or subtracting terms that have the same variables raised to the same powers.
- Distributive Property: You can distribute a multiplication over addition, shown as $a(b + c) = ab + ac$.
- Translating Words into Expressions: Converting phrases into mathematical expressions. For example, "the sum of a number and 5" translates to $x + 5$.
- Equivalent Expressions: Two expressions that yield the same value for any value of their variables.
- Evaluating Expressions: Finding the value of an expression by substituting in values for the variables.
-
Practice Examples for Clarity
Use practice examples to demonstrate each concept. For instance:
- For exponents, compute $2^3 = 2 \times 2 \times 2 = 8$.
- Combine like terms in $3x + 5x = 8x$.
- Apply the distributive property in $2(3 + 4) = 2 \cdot 3 + 2 \cdot 4 = 6 + 8 = 14$.
-
Solve an Expression Example
Choose an example expression, for instance, $3(x + 2) + 4x$.
First, apply the distributive property:
$$ 3(x + 2) = 3x + 6 $$
Then, combine like terms:
$$ 3x + 6 + 4x = 7x + 6 $$
This gives us the final simplified expression.
The final simplified expression is $7x + 6$.
More Information
The answer highlights how to effectively use mathematical concepts to simplify complex expressions. It's crucial to practice these skills to gain fluency in algebra.
Tips
- Not applying the distributive property correctly, leading to incorrect expressions.
- Forgetting to combine like terms, which can result in an incomplete answer.
- Misinterpreting word problems and translating them incorrectly into algebraic expressions.
AI-generated content may contain errors. Please verify critical information