Evaluate The Expression X ( Y + 3 ) ( 3 + Y ) Z {\frac{x(y+3)}{(3+y) Z}} ( 3 + Y ) Z X ( Y + 3 ) ​ For X = 6 {x = 6} X = 6 , Y = 9 {y = 9} Y = 9 , And Z = 2 {z = 2} Z = 2 . A. 4 B. 5 C. 6 D. 3

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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 evaluate the expression x(y+3)(3+y)z{\frac{x(y+3)}{(3+y) z}} for specific values of x{x}, y{y}, and z{z}. We will break down the process into manageable steps, making it easy to understand and follow.

Understanding the Expression

The given expression is x(y+3)(3+y)z{\frac{x(y+3)}{(3+y) z}}. To evaluate this expression, we need to substitute the given values of x{x}, y{y}, and z{z} into the expression. Let's start by identifying the values of x{x}, y{y}, and z{z}.

Given Values

  • x=6{x = 6}
  • y=9{y = 9}
  • z=2{z = 2}

Substituting Values into the Expression

Now that we have the given values, we can substitute them into the expression. We will replace x{x}, y{y}, and z{z} with their respective values.

Substituted Expression

6(9+3)(3+9)2{\frac{6(9+3)}{(3+9) 2}}

Simplifying the Expression

The next step is to simplify the expression by performing the operations inside the parentheses and then multiplying and dividing from left to right.

Simplified Expression

6(12)(12)2{\frac{6(12)}{(12) 2}}

Evaluating the Expression

Now that we have a simplified expression, we can evaluate it by performing the multiplication and division operations.

Evaluated Expression

7224{\frac{72}{24}}

Final Answer

To get the final answer, we need to simplify the fraction by dividing the numerator by the denominator.

Final Answer

7224=3{\frac{72}{24} = 3}

Conclusion

Evaluating algebraic expressions is a crucial skill for students to master. By following the steps outlined in this article, we can easily evaluate the expression x(y+3)(3+y)z{\frac{x(y+3)}{(3+y) z}} for specific values of x{x}, y{y}, and z{z}. Remember to substitute the given values into the expression, simplify it, and then evaluate it to get the final answer.

Frequently Asked Questions

Q: What is the final answer to the expression x(y+3)(3+y)z{\frac{x(y+3)}{(3+y) z}} for x=6{x = 6}, y=9{y = 9}, and z=2{z = 2}?

A: The final answer is 3.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the given values into the expression, simplify it, and then evaluate it to get the final answer.

Q: What is the importance of evaluating algebraic expressions?

A: Evaluating algebraic expressions is a crucial skill for students to master, as it helps them to solve problems in mathematics and real-life situations.

References

Related Articles

Discussion

  • What is the most challenging part of evaluating algebraic expressions?
  • How do you simplify an algebraic expression?
  • What is the importance of evaluating algebraic expressions in real-life situations?

Note: The discussion category is mathematics.

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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 the expression x(y+3)(3+y)z{\frac{x(y+3)}{(3+y) z}} for specific values of x{x}, y{y}, and z{z}. In this article, we will answer some frequently asked questions about evaluating algebraic expressions.

Q&A

Q: What is the most challenging part of evaluating algebraic expressions?

A: The most challenging part of evaluating algebraic expressions is simplifying the expression. This involves performing operations inside the parentheses, multiplying and dividing from left to right, and then simplifying the resulting fraction.

Q: How do you simplify an algebraic expression?

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

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate 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 importance of evaluating algebraic expressions in real-life situations?

A: Evaluating algebraic expressions is essential in real-life situations, such as:

  • Science: Algebraic expressions are used to model real-world phenomena, such as population growth and chemical reactions.
  • Engineering: Algebraic expressions are used to design and optimize systems, such as bridges and electronic circuits.
  • Finance: Algebraic expressions are used to calculate interest rates and investment returns.

Q: How do you evaluate an algebraic expression with variables?

A: To evaluate an algebraic expression with variables, you need to substitute the given values into the expression and then simplify it.

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

A: An algebraic expression is a mathematical statement that contains variables and constants, while an equation is a statement that says two expressions are equal.

Q: How do you solve an equation with an algebraic expression?

A: To solve an equation with an algebraic expression, you need to isolate the variable by performing inverse operations.

Examples

Example 1: Evaluating an Algebraic Expression

Evaluate the expression x+2x−3{\frac{x+2}{x-3}} for x=5{x = 5}.

Solution

5+25−3=72{\frac{5+2}{5-3} = \frac{7}{2}}

Example 2: Simplifying an Algebraic Expression

Simplify the expression 2x2+3x−1x2−4{\frac{2x^2 + 3x - 1}{x^2 - 4}}.

Solution

2x2+3x−1x2−4=(2x−1)(x+1)(x−2)(x+2){\frac{2x^2 + 3x - 1}{x^2 - 4} = \frac{(2x - 1)(x + 1)}{(x - 2)(x + 2)}}

Conclusion

Evaluating algebraic expressions is a crucial skill for students to master. By following the steps outlined in this article, you can easily evaluate algebraic expressions and simplify them to get the final answer. Remember to substitute the given values into the expression, simplify it, and then evaluate it to get the final answer.

Frequently Asked Questions

Q: What is the final answer to the expression x(y+3)(3+y)z{\frac{x(y+3)}{(3+y) z}} for x=6{x = 6}, y=9{y = 9}, and z=2{z = 2}?

A: The final answer is 3.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the given values into the expression, simplify it, and then evaluate it to get the final answer.

Q: What is the importance of evaluating algebraic expressions?

A: Evaluating algebraic expressions is a crucial skill for students to master, as it helps them to solve problems in mathematics and real-life situations.

References

Related Articles

Discussion

  • What is the most challenging part of evaluating algebraic expressions?
  • How do you simplify an algebraic expression?
  • What is the importance of evaluating algebraic expressions in real-life situations?