Evaluate Each Algebraic Expression For The Given Value Of { X $}$.5) { -6.2x + 1.4x$}$, { X = -9.3$}$6) ${ 3 \frac{1}{2}x - 5 \frac{1}{3}x\$} , { X = \frac{2}{5}$}$

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 algebraic expressions for given values of the variable. We will use two examples to demonstrate the process, and provide a step-by-step guide to help students understand the concept.

Example 1: Evaluating a Linear Expression

Problem Statement

Evaluate the algebraic expression ${-6.2x + 1.4x}$ for ${x = -9.3}$.

Solution

To evaluate the expression, we need to substitute the given value of ${x}$ into the expression.

${-6.2x + 1.4x = -6.2(-9.3) + 1.4(-9.3)}$

Now, we need to simplify the expression by multiplying the coefficients with the variable.

${-6.2(-9.3) = 57.66}$ ${1.4(-9.3) = -13.02}$

Next, we need to add the two terms together.

${57.66 - 13.02 = 44.64}$

Therefore, the value of the expression is ${44.64}$.

Explanation

In this example, we used the distributive property to simplify the expression. We multiplied the coefficients with the variable and then added the two terms together. This is a common technique used to evaluate algebraic expressions.

Example 2: Evaluating a Mixed Expression

Problem Statement

Evaluate the algebraic expression ${3 \frac{1}{2}x - 5 \frac{1}{3}x}$ for ${x = \frac{2}{5}}$.

Solution

To evaluate the expression, we need to substitute the given value of ${x}$ into the expression.

${3 \frac{1}{2}x - 5 \frac{1}{3}x = 3.5x - 5.33x}$

Now, we need to simplify the expression by multiplying the coefficients with the variable.

${3.5x = 3.5 \times \frac{2}{5} = 1.4}$ ${5.33x = 5.33 \times \frac{2}{5} = 2.132}$

Next, we need to subtract the two terms together.

${1.4 - 2.132 = -0.732}$

Therefore, the value of the expression is ${-0.732}$.

Explanation

In this example, we used the distributive property to simplify the expression. We multiplied the coefficients with the variable and then subtracted the two terms together. This is a common technique used to evaluate algebraic expressions.

Tips and Tricks

• Always substitute the given value of the variable into the expression.
• Simplify the expression by multiplying the coefficients with the variable.
• Use the distributive property to simplify the expression.
• Add or subtract the terms together as required.

Conclusion

Evaluating algebraic expressions is a crucial skill for students to master. By following the steps outlined in this article, students can evaluate expressions with confidence. Remember to substitute the given value of the variable into the expression, simplify the expression by multiplying the coefficients with the variable, and use the distributive property to simplify the expression. With practice, students can become proficient in evaluating algebraic expressions.

Common Mistakes to Avoid

• Not substituting the given value of the variable into the expression.
• Not simplifying the expression by multiplying the coefficients with the variable.
• Not using the distributive property to simplify the expression.

Real-World Applications

Evaluating algebraic expressions has many real-world applications. For example, in physics, algebraic expressions are used to describe the motion of objects. In engineering, algebraic expressions are used to design and optimize systems. In economics, algebraic expressions are used to model and analyze economic systems.

Practice Problems

1. Evaluate the algebraic expression ${2x + 5x}$ for ${x = 3}$.
2. Evaluate the algebraic expression ${4 \frac{1}{2}x - 2 \frac{1}{3}x}$ for ${x = \frac{1}{2}}$.
3. Evaluate the algebraic expression ${x^2 + 2x + 1}$ for ${x = 2}$.

Answer Key

1. ${7x}$ = ${21}$
2. ${3.33x - 1.33x}$ = ${2x}$ = ${1}$
3. ${(2)^2 + 2(2) + 1}$ = ${4 + 4 + 1}$ = ${9}$

Conclusion

Introduction

Evaluating algebraic expressions is a crucial skill for students to master. In our previous article, we provided a step-by-step guide on how to evaluate algebraic expressions. In this article, we will answer some frequently asked questions (FAQs) on 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 to represent a mathematical relationship between variables and constants.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the given value of the variable into the expression, simplify the expression by multiplying the coefficients with the variable, and use the distributive property to simplify the expression.

Q: What is the distributive property?

A: The distributive property is a mathematical property that allows you to multiply a single term by multiple terms. It is used to simplify algebraic expressions.

Q: How do I use the distributive property to simplify an algebraic expression?

A: To use the distributive property to simplify an algebraic expression, you need to multiply the coefficients with the variable and then add or subtract the terms together as required.

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

A: Some common mistakes to avoid when evaluating algebraic expressions include not substituting the given value of the variable into the expression, not simplifying the expression by multiplying the coefficients with the variable, and not using the distributive property to simplify the expression.

Q: How do I evaluate an algebraic expression with multiple variables?

A: To evaluate an algebraic expression with multiple variables, you need to substitute the given values of the variables into the expression, simplify the expression by multiplying the coefficients with the variables, and use the distributive property to simplify the expression.

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

A: Evaluating algebraic expressions has many real-world applications, including physics, engineering, and economics. In physics, algebraic expressions are used to describe the motion of objects. In engineering, algebraic expressions are used to design and optimize systems. In economics, algebraic expressions are used to model and analyze economic systems.

Q: How do I practice evaluating algebraic expressions?

A: You can practice evaluating algebraic expressions by working through practice problems, such as those found in textbooks or online resources. You can also try evaluating algebraic expressions on your own by creating your own problems and solutions.

Q: What are some resources available to help me learn how to evaluate algebraic expressions?

A: There are many resources available to help you learn how to evaluate algebraic expressions, including textbooks, online tutorials, and practice problems. You can also seek help from a teacher or tutor if you are struggling with the concept.

Conclusion

Evaluating algebraic expressions is a crucial skill for students to master. By following the steps outlined in this article, you can evaluate expressions with confidence. Remember to substitute the given value of the variable into the expression, simplify the expression by multiplying the coefficients with the variable, and use the distributive property to simplify the expression. With practice, you can become proficient in evaluating algebraic expressions.

Practice Problems

1. Evaluate the algebraic expression ${2x + 5x}$ for ${x = 3}$.
2. Evaluate the algebraic expression ${4 \frac{1}{2}x - 2 \frac{1}{3}x}$ for ${x = \frac{1}{2}}$.
3. Evaluate the algebraic expression ${x^2 + 2x + 1}$ for ${x = 2}$.

Answer Key

1. ${7x}$ = ${21}$
2. ${3.33x - 1.33x}$ = ${2x}$ = ${1}$
3. ${(2)^2 + 2(2) + 1}$ = ${4 + 4 + 1}$ = ${9}$

Additional Resources

• Khan Academy: Algebraic Expressions
• Mathway: Algebraic Expressions
• IXL: Algebraic Expressions

Conclusion

Evaluating algebraic expressions is a crucial skill for students to master. By following the steps outlined in this article, you can evaluate expressions with confidence. Remember to substitute the given value of the variable into the expression, simplify the expression by multiplying the coefficients with the variable, and use the distributive property to simplify the expression. With practice, you can become proficient in evaluating algebraic expressions.