Evaluate And Match Each Expression On The Left To Its Value On The Right, When $x=7$ And $y=4$.$\[ \begin{array}{ll} 12+x & 19 \\ 3x+y & 25 \\ 4y-10 & 6 \\ \frac{1}{2}xy & 14 \\ \end{array} \\]

Introduction

Algebraic expressions are a fundamental concept in mathematics, and evaluating them is a crucial skill for students to master. In this article, we will explore how to evaluate and match each expression on the left to its value on the right, given the values of $x$ and $y$. We will use the given expressions and values to demonstrate the step-by-step process of evaluating algebraic expressions.

Understanding the Given Expressions

We are given four algebraic expressions and their corresponding values:

Expression	Value
$12+x$	19
$3x+y$	25
$4y-10$	6
$\frac{1}{2}xy$	14

Evaluating the First Expression: $12+x$

To evaluate the first expression, we need to substitute the value of $x$ into the expression. We are given that $x=7$, so we can substitute this value into the expression as follows:

$$12+x=12+7=19$$

Therefore, the value of the first expression is 19.

Evaluating the Second Expression: $3x+y$

To evaluate the second expression, we need to substitute the values of $x$ and $y$ into the expression. We are given that $x=7$ and $y=4$, so we can substitute these values into the expression as follows:

$$3x+y=3(7)+4=21+4=25$$

Therefore, the value of the second expression is 25.

Evaluating the Third Expression: $4y-10$

To evaluate the third expression, we need to substitute the value of $y$ into the expression. We are given that $y=4$, so we can substitute this value into the expression as follows:

$$4y-10=4(4)-10=16-10=6$$

Therefore, the value of the third expression is 6.

Evaluating the Fourth Expression: $\frac{1}{2}xy$

To evaluate the fourth expression, we need to substitute the values of $x$ and $y$ into the expression. We are given that $x=7$ and $y=4$, so we can substitute these values into the expression as follows:

$$\frac{1}{2}xy=\frac{1}{2}(7)(4)=14$$

Therefore, the value of the fourth expression is 14.

Conclusion

In this article, we have evaluated and matched each expression on the left to its value on the right, given the values of $x$ and $y$. We have demonstrated the step-by-step process of evaluating algebraic expressions using the given expressions and values. By following these steps, students can master the skill of evaluating algebraic expressions and apply it to a wide range of mathematical problems.

Tips and Tricks

• Always substitute the given values into the expression.
• Follow the order of operations (PEMDAS) when evaluating expressions.
• Simplify the expression before evaluating it.
• Check your work by plugging the value back into the original expression.

Common Mistakes to Avoid

• Failing to substitute the given values into the expression.
• Not following the order of operations (PEMDAS).
• Not simplifying the expression before evaluating it.
• Not checking your work by plugging the value back into the original expression.

Real-World Applications

Evaluating algebraic expressions has numerous real-world applications, including:

• Science: Algebraic expressions are used to model real-world phenomena, such as the motion of objects and the behavior of populations.
• Engineering: Algebraic expressions are used to design and optimize systems, such as bridges and electronic circuits.
• Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.

Conclusion

$$$$

Introduction

In our previous article, we explored how to evaluate and match each expression on the left to its value on the right, given the values of $x$ and $y$. In this article, we will answer some of the most frequently asked questions about evaluating algebraic expressions.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that contains variables, constants, and mathematical operations. It is a way of representing a mathematical relationship between variables and constants.

Q: What are the steps to evaluate an algebraic expression?

A: The steps to evaluate an algebraic expression are:

1. Substitute the given values into the expression.
2. Follow the order of operations (PEMDAS).
3. Simplify the expression before evaluating it.
4. Check your work by plugging the value back into the original expression.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when evaluating an expression. PEMDAS stands for:

• 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 algebraic expression?

A: To simplify an algebraic expression, you can combine like terms and eliminate any unnecessary operations. For example, if you have the expression $2x + 3x$, you can combine the like terms to get $5x$.

Q: What are some common mistakes to avoid when evaluating algebraic expressions?

A: Some common mistakes to avoid when evaluating algebraic expressions include:

• Failing to substitute the given values into the expression.
• Not following the order of operations (PEMDAS).
• Not simplifying the expression before evaluating it.
• Not checking your work by plugging the value back into the original expression.

Q: How do I check my work when evaluating an algebraic expression?

A: To check your work when evaluating an algebraic expression, you can plug the value back into the original expression and see if it matches the value you obtained. For example, if you evaluated the expression $2x + 3$ and obtained the value 5, you can plug $x=1$ back into the original expression to get $2(1) + 3 = 5$, which matches the value you obtained.

Q: What are some real-world applications of evaluating algebraic expressions?

A: Evaluating algebraic expressions has numerous real-world applications, including:

• Science: Algebraic expressions are used to model real-world phenomena, such as the motion of objects and the behavior of populations.
• Engineering: Algebraic expressions are used to design and optimize systems, such as bridges and electronic circuits.
• Economics: Algebraic expressions are used to model economic systems and make predictions about future trends.

Conclusion

In conclusion, evaluating algebraic expressions is a crucial skill for students to master. By following the step-by-step process outlined in this article and avoiding common mistakes, students can develop the skills and confidence needed to tackle a wide range of mathematical problems. With practice and patience, students can become proficient in evaluating algebraic expressions and apply it to real-world applications.