Unlocking the Mystery: Lesson 6.1 Algebraic Expressions Answer Key Revealed

Unlocking the Mystery: Lesson 6.1 Algebraic Expressions Answer Key Revealed

If you’re feeling overwhelmed by algebraic expressions, you’re not alone. Many math students struggle with this topic, but it doesn’t have to be a mystery. In this article, we’ll unlock the secret to Lesson 6.1 Algebraic Expressions and reveal the answer key.

Introduction

Before we delve into the answer key, let’s quickly recap the basics of algebraic expressions. An algebraic expression is a combination of numbers, variables, and operations. For example, 3x + 2 is an algebraic expression. The variable x can take on different values, and the operations (addition and multiplication) determine how the expression is evaluated. To simplify algebraic expressions, we use the order of operations and various algebraic techniques.

Body

Lesson 6.1 Algebraic Expressions covers the following topics:

– Evaluating algebraic expressions
– Writing algebraic expressions from word problems
– Identifying parts of an algebraic expression (coefficients, variables, exponents, and constants)
– Simplifying algebraic expressions using the distributive property and combining like terms.

To evaluate an algebraic expression, substitute the given values for the variables and simplify the expression. For example, if x = 2 and y = 3, evaluate 5x – 2y by substituting x and y, and then simplifying the expression:

5x – 2y = 5(2) – 2(3) = 10 – 6 = 4

To write an algebraic expression from a word problem, identify the variables and the operations involved. Then, translate the problem into an algebraic expression. For example, if the problem states “Twice a number increased by three is eight,” the algebraic expression is 2x + 3 = 8, where x is the unknown number.

Identifying parts of an algebraic expression is crucial for simplification. The coefficient is the number that appears before a variable (e.g., 3x, where 3 is the coefficient). The variable is the letter that represents an unknown value (e.g., x). The exponent is the number that indicates repeated multiplication (e.g., 4×2, where 2 is the exponent). The constant is the number that does not change (e.g., 5).

To simplify algebraic expressions, we use the distributive property (multiplying a number outside the parentheses with each term inside the parentheses) and combine like terms (terms that have the same variables and exponents). For example, simplify the expression 2(3x + 4) – 5x + 2x + 8 as follows:

2(3x + 4) – 5x + 2x + 8 = 6x + 8 – 5x + 2x + 8
= 3x + 16

Now that we’ve reviewed the basics of Lesson 6.1 Algebraic Expressions, let’s reveal the answer key.

Answer Key

Here are the answers to some practice problems in Lesson 6.1 Algebraic Expressions:

1. Evaluate 4x – 3y, where x = 2 and y = 5
Answer: 2

2. Write an algebraic expression for the following problem: Five times a number decreased by two is 23.
Answer: 5x – 2 = 23

3. Identify the coefficient, variable, and constant in the following expression: 7n + 5
Answer: Coefficient: 7, Variable: n, Constant: 5

4. Simplify the expression 2(3x – 4) + 5x – 7
Answer: 11x – 15

Conclusion

Algebraic expressions can be tricky, but with practice and understanding of the basics, you’ll be able to unlock the mystery of Lesson 6.1 Algebraic Expressions. Remember to evaluate, write, identify, and simplify algebraic expressions using the order of operations and various techniques. We hope this article has helped you to better understand this important concept in math.

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