Introduction
Algebra 2 is a fundamental subject that builds upon the concepts learned in Algebra 1. Lesson 1.1 is the starting point for many students as they embark on their algebraic journey. In this article, we will provide an answer key for Lesson 1.1, which covers topics such as evaluating algebraic expressions, simplifying expressions, and solving equations. Whether you are a student looking for guidance or a teacher seeking additional resources, this answer key will serve as a valuable tool to enhance your understanding of algebraic concepts.
Evaluating Algebraic Expressions
One of the first skills students learn in Algebra 2 is how to evaluate algebraic expressions. This involves substituting values for variables and simplifying the expression to find the numerical result. The answer key for Lesson 1.1 will provide step-by-step solutions to various problems related to evaluating algebraic expressions. By following these solutions, students can gain a clear understanding of the process and develop their problem-solving skills.
Example 1
Problem: Evaluate the expression 3x + 2y when x = 4 and y = -1.
Solution: To evaluate the expression, substitute the given values for x and y into the expression: 3(4) + 2(-1). Simplify the expression by performing the multiplication and addition: 12 - 2 = 10. Therefore, the value of the expression 3x + 2y when x = 4 and y = -1 is 10.
Example 2
Problem: Evaluate the expression 2a^2 - 3b + c when a = -2, b = 5, and c = 1.
Solution: Substituting the given values into the expression, we have: 2(-2)^2 - 3(5) + 1. Simplifying the expression: 2(4) - 15 + 1 = 8 - 15 + 1 = -6. Therefore, the value of the expression 2a^2 - 3b + c when a = -2, b = 5, and c = 1 is -6.
Simplifying Expressions
Another important concept in Algebra 2 is simplifying expressions. This involves combining like terms, using the distributive property, and applying other algebraic rules to make the expression as concise as possible. The answer key for Lesson 1.1 will provide detailed explanations and examples of how to simplify various types of expressions.
Example 1
Problem: Simplify the expression 5x + 3x - 2y + 4x - y.
Solution: To simplify the expression, combine the like terms: 5x + 3x + 4x - 2y - y. This simplifies to 12x - 3y. Therefore, the simplified form of the expression 5x + 3x - 2y + 4x - y is 12x - 3y.
Example 2
Problem: Simplify the expression 2(3x - 4) + 5(2x + 1).
Solution: Using the distributive property, we can simplify the expression: 2(3x) - 2(4) + 5(2x) + 5(1). This simplifies to 6x - 8 + 10x + 5. Combining like terms, we have 16x - 3. Therefore, the simplified form of the expression 2(3x - 4) + 5(2x + 1) is 16x - 3.
Solving Equations
Solving equations is a fundamental skill in algebra. Lesson 1.1 introduces students to the process of solving linear equations with one variable. The answer key will provide step-by-step solutions to equations of varying difficulty, helping students grasp the underlying concepts and techniques.
Example 1
Problem: Solve the equation 2x + 5 = 17.
Solution: To solve the equation, isolate the variable by performing the necessary operations. Start by subtracting 5 from both sides: 2x + 5 - 5 = 17 - 5, which simplifies to 2x = 12. Next, divide both sides by 2 to solve for x: 2x/2 = 12/2, resulting in x = 6. Therefore, the solution to the equation 2x + 5 = 17 is x = 6.
Example 2
Problem: Solve the equation 3(2x + 4) - 5 = 13.
Solution: Begin by simplifying the expression within the parentheses using the distributive property: 3(2x) + 3(4) - 5 = 6x + 12 - 5. This simplifies to 6x + 7 - 5 = 13. Combine like terms to further simplify the equation: 6x + 2 = 13. Next, subtract 2 from both sides: 6x + 2 - 2 = 13 - 2, resulting in 6x = 11. Finally, divide both sides by 6 to solve for x: 6x/6 = 11/6, giving us x = 11/6. Therefore, the solution to the equation 3(2x + 4) - 5 = 13 is x = 11/6.
Conclusion
Algebra 2 Lesson 1.1 covers essential topics such as evaluating algebraic expressions, simplifying expressions, and solving equations. The answer key provided in this article serves as a valuable resource for students and teachers alike. By following the step-by-step solutions and examples, students can deepen their understanding of algebraic concepts and improve their problem-solving skills. Teachers can also utilize this answer key as a tool to assess student understanding and provide additional support when necessary. With this comprehensive answer key, students can confidently navigate the challenges of Algebra 2 Lesson 1.1 and lay a strong foundation for future success in algebra.