Evaluate The Following Expressions When { Y = -2 $}$.1. { Y - 3 $}$2. { 2y - 5 $}$
Introduction
In algebra, evaluating expressions with a given variable value is a crucial skill that helps us solve equations and inequalities. In this article, we will evaluate two algebraic expressions when the variable y is equal to -2. We will use the given value of y to substitute into the expressions and simplify them.
Expression 1: y - 3
The first expression is y - 3. To evaluate this expression, we need to substitute the value of y, which is -2, into the expression.
Substituting y = -2 into the Expression
When y = -2, the expression y - 3 becomes:
-2 - 3
Simplifying the Expression
To simplify the expression, we need to combine the two terms.
-2 - 3 = -5
Therefore, the value of the expression y - 3 when y = -2 is -5.
Expression 2: 2y - 5
The second expression is 2y - 5. To evaluate this expression, we need to substitute the value of y, which is -2, into the expression.
Substituting y = -2 into the Expression
When y = -2, the expression 2y - 5 becomes:
2(-2) - 5
Simplifying the Expression
To simplify the expression, we need to follow the order of operations (PEMDAS):
- Multiply 2 and -2: 2(-2) = -4
- Subtract 5 from -4: -4 - 5 = -9
Therefore, the value of the expression 2y - 5 when y = -2 is -9.
Conclusion
In this article, we evaluated two algebraic expressions when the variable y was equal to -2. We used the given value of y to substitute into the expressions and simplify them. The first expression, y - 3, simplified to -5, and the second expression, 2y - 5, simplified to -9. These results demonstrate the importance of following the order of operations and simplifying expressions with given variable values.
Real-World Applications
Evaluating algebraic expressions with given variable values has numerous real-world applications. For example, in physics, we use algebraic expressions to describe the motion of objects. In economics, we use algebraic expressions to model the behavior of markets. In computer science, we use algebraic expressions to write algorithms and solve problems.
Tips and Tricks
When evaluating algebraic expressions with given variable values, remember to:
- Follow the order of operations (PEMDAS)
- Simplify expressions by combining like terms
- Use the given value of the variable to substitute into the expression
- Check your work by plugging the value back into the expression
By following these tips and tricks, you will become proficient in evaluating algebraic expressions with given variable values and be able to apply this skill to a wide range of real-world problems.
Common Mistakes
When evaluating algebraic expressions with given variable values, common mistakes include:
- Forgetting to follow the order of operations (PEMDAS)
- Not simplifying expressions by combining like terms
- Substituting the wrong value of the variable into the expression
- Not checking your work by plugging the value back into the expression
To avoid these mistakes, make sure to carefully read the problem, follow the order of operations, and simplify expressions by combining like terms.
Practice Problems
To practice evaluating algebraic expressions with given variable values, try the following problems:
- Evaluate the expression 3y + 2 when y = 4.
- Evaluate the expression 2y - 1 when y = -3.
- Evaluate the expression y^2 + 5 when y = 2.
Introduction
In our previous article, we evaluated two algebraic expressions when the variable y was equal to -2. We used the given value of y to substitute into the expressions and simplify them. In this article, we will answer some frequently asked questions about evaluating algebraic expressions with given variable values.
Q: What is the order of operations?
A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I simplify an expression with multiple terms?
A: To simplify an expression with multiple terms, combine like terms. Like terms are terms that have the same variable and exponent. For example, 2x and 3x are like terms, but 2x and 5 are not.
Q: What is the difference between a variable and a constant?
A: A variable is a letter or symbol that represents a value that can change. A constant is a value that does not change. For example, x is a variable, but 5 is a constant.
Q: How do I evaluate an expression with a negative exponent?
A: To evaluate an expression with a negative exponent, use the rule that a^(-n) = 1/a^n. For example, 2^(-3) = 1/2^3 = 1/8.
Q: Can I evaluate an expression with a variable that is not defined?
A: No, you cannot evaluate an expression with a variable that is not defined. You must first define the variable before you can evaluate the expression.
Q: How do I evaluate an expression with multiple variables?
A: To evaluate an expression with multiple variables, substitute the values of the variables into the expression and simplify. For example, if the expression is 2x + 3y and x = 4 and y = 2, then the expression becomes 2(4) + 3(2) = 8 + 6 = 14.
Q: Can I use a calculator to evaluate an expression?
A: Yes, you can use a calculator to evaluate an expression. However, make sure to check your work by plugging the value back into the expression.
Q: How do I check my work when evaluating an expression?
A: To check your work, plug the value back into the expression and simplify. If the result is the same as the original expression, then your work is correct.
Conclusion
Evaluating algebraic expressions with given variable values is an important skill that has numerous real-world applications. By following the order of operations, simplifying expressions by combining like terms, and checking your work, you can become proficient in evaluating algebraic expressions with given variable values.
Practice Problems
To practice evaluating algebraic expressions with given variable values, try the following problems:
- Evaluate the expression 2x + 3y when x = 4 and y = 2.
- Evaluate the expression 3x - 2y when x = 5 and y = 3.
- Evaluate the expression x^2 + 2y when x = 2 and y = 4.
Remember to follow the order of operations and simplify expressions by combining like terms.