Maria Determined That These Expressions Are Equivalent Using The Values Of X = 3 X=3 X = 3 And X = 7 X=7 X = 7 . Which Statements Are True? Check All That Apply.Expressions:- 5 + 3 X − 2 5 + 3x - 2 5 + 3 X − 2 - X + 2 ( X + 1 ) + 1 X + 2(x+1) + 1 X + 2 ( X + 1 ) + 1 Options:- The Expressions Are

Introduction

In mathematics, expressions are a fundamental concept that helps us represent mathematical relationships between variables and constants. When evaluating expressions, it's essential to understand the properties of algebraic expressions, such as the distributive property, the associative property, and the commutative property. In this article, we'll delve into the world of expressions and explore the statements that are true based on the given expressions and values of $x$.

Understanding the Expressions

The two expressions given are:

1. $5 + 3x - 2$
2. $x + 2(x+1) + 1$

To determine which statements are true, we need to evaluate these expressions using the values of $x=3$ and $x=7$.

Evaluating Expression 1

Let's start by evaluating expression 1 using the values of $x=3$ and $x=7$.

x = 3

Substituting $x=3$ into expression 1, we get:

$5 + 3(3) - 2$

Using the distributive property, we can rewrite this as:

$5 + 9 - 2$

Evaluating the expression, we get:

$5 + 9 - 2 = 12$

x = 7

Substituting $x=7$ into expression 1, we get:

$5 + 3(7) - 2$

Using the distributive property, we can rewrite this as:

$5 + 21 - 2$

Evaluating the expression, we get:

$5 + 21 - 2 = 24$

Evaluating Expression 2

Now, let's evaluate expression 2 using the values of $x=3$ and $x=7$.

x = 3

Substituting $x=3$ into expression 2, we get:

$3 + 2(3+1) + 1$

Using the distributive property, we can rewrite this as:

$3 + 2(4) + 1$

Evaluating the expression, we get:

$3 + 8 + 1 = 12$

x = 7

Substituting $x=7$ into expression 2, we get:

$7 + 2(7+1) + 1$

Using the distributive property, we can rewrite this as:

$7 + 2(8) + 1$

Evaluating the expression, we get:

$7 + 16 + 1 = 24$

Comparing the Results

Now that we have evaluated both expressions using the values of $x=3$ and $x=7$, let's compare the results.

Expression	x = 3	x = 7
Expression 1	12	24
Expression 2	12	24

As we can see, both expressions evaluate to the same values for both $x=3$ and $x=7$. This suggests that the expressions are equivalent.

Conclusion

In conclusion, based on the evaluations of the expressions using the values of $x=3$ and $x=7$, we can determine that the following statements are true:

• The expressions are equivalent.
• The expressions have the same value for both $x=3$ and $x=7$.

Therefore, the correct answer is:

• The expressions are equivalent.

Final Thoughts

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Q&A: Evaluating Expressions

In the previous article, we explored the world of expressions and evaluated two given expressions using the values of $x=3$ and $x=7$. We found that the expressions are equivalent and have the same value for both $x=3$ and $x=7$. In this article, we'll answer some frequently asked questions about evaluating expressions.

Q: What is an expression in mathematics?

A: An expression in mathematics is a combination of variables, constants, and mathematical operations that can be evaluated to a single value. Expressions can be simple, such as $2x + 3$, or complex, such as $x^2 + 3x - 2$.

Q: What are the properties of algebraic expressions?

A: Algebraic expressions have several properties, including:

• Distributive property: This property states that for any numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.
• Associative property: This property states that for any numbers $a$, $b$, and $c$, $(a + b) + c = a + (b + c)$.
• Commutative property: This property states that for any numbers $a$ and $b$, $a + b = b + a$.

Q: How do I evaluate an expression?

A: To evaluate an expression, you need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate any expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between an expression and an equation?

A: An expression is a combination of variables, constants, and mathematical operations that can be evaluated to a single value. An equation, on the other hand, is a statement that two expressions are equal. For example, $2x + 3 = 5$ is an equation, while $2x + 3$ is an expression.

Q: How do I simplify an expression?

A: To simplify an expression, you need to apply the properties of algebraic expressions, such as the distributive property, associative property, and commutative property. You can also combine like terms and eliminate any unnecessary operations.

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

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

• Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when evaluating expressions.
• Not simplifying expressions: Simplify expressions as much as possible to make them easier to evaluate.
• Not checking for errors: Double-check your work to ensure that you have evaluated the expression correctly.

Conclusion

Evaluating expressions is a crucial skill in mathematics, and understanding the properties of algebraic expressions is essential for solving problems. By following the order of operations, simplifying expressions, and avoiding common mistakes, you can become proficient in evaluating expressions. In this article, we answered some frequently asked questions about evaluating expressions and provided tips and tricks for simplifying expressions.