Evaluate Each Expression If $x=3, Y=12,$ And $z=8$.12. $4z + 8 - 6$13. $ 7 Z ÷ 4 + 5 X 7z \div 4 + 5x 7 Z ÷ 4 + 5 X [/tex]14. $y^2 \div (3z)$

by ADMIN 150 views

In this article, we will evaluate three algebraic expressions given the values of variables x, y, and z. We will substitute the given values into each expression and simplify to find the final result.

Given Values

  • x = 3
  • y = 12
  • z = 8

Expression 1: 4z + 8 - 6

To evaluate this expression, we will substitute the value of z into the expression and then perform the arithmetic operations.

Step 1: Substitute the value of z

4z + 8 - 6 = 4(8) + 8 - 6

Step 2: Multiply 4 and 8

4(8) = 32

Step 3: Add 8 and 32

32 + 8 = 40

Step 4: Subtract 6 from 40

40 - 6 = 34

Final Result for Expression 1

The final result for expression 1 is 34.

Expression 2: 7z ÷ 4 + 5x

To evaluate this expression, we will substitute the values of z and x into the expression and then perform the arithmetic operations.

Step 1: Substitute the values of z and x

7z ÷ 4 + 5x = 7(8) ÷ 4 + 5(3)

Step 2: Multiply 7 and 8

7(8) = 56

Step 3: Divide 56 by 4

56 ÷ 4 = 14

Step 4: Multiply 5 and 3

5(3) = 15

Step 5: Add 14 and 15

14 + 15 = 29

Final Result for Expression 2

The final result for expression 2 is 29.

Expression 3: y^2 ÷ (3z)

To evaluate this expression, we will substitute the values of y and z into the expression and then perform the arithmetic operations.

Step 1: Substitute the values of y and z

y^2 ÷ (3z) = (12)^2 ÷ (3(8))

Step 2: Square 12

(12)^2 = 144

Step 3: Multiply 3 and 8

3(8) = 24

Step 4: Divide 144 by 24

144 ÷ 24 = 6

Final Result for Expression 3

The final result for expression 3 is 6.

Conclusion

In this article, we evaluated three algebraic expressions given the values of variables x, y, and z. We substituted the given values into each expression and simplified to find the final result. The final results for the expressions are 34, 29, and 6, respectively.

Key Takeaways

  • To evaluate algebraic expressions, we need to substitute the given values into the expression and then perform the arithmetic operations.
  • We need to follow the order of operations (PEMDAS) when simplifying expressions.
  • We can use variables to represent unknown values and then substitute the values into the expression to find the final result.

Future Applications

Evaluating algebraic expressions is a fundamental concept in mathematics and has numerous applications in various fields, including science, engineering, economics, and computer science. By understanding how to evaluate algebraic expressions, we can solve problems in these fields and make informed decisions.

Common Mistakes to Avoid

When evaluating algebraic expressions, we need to avoid common mistakes such as:

  • Not following the order of operations (PEMDAS)
  • Not substituting the given values into the expression
  • Not simplifying the expression correctly

By avoiding these mistakes, we can ensure that our final results are accurate and reliable.

Real-World Examples

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

  • Calculating the cost of goods and services
  • Determining the area and perimeter of shapes
  • Solving problems in physics and engineering
  • Analyzing data in economics and finance

By understanding how to evaluate algebraic expressions, we can solve problems in these fields and make informed decisions.

Final Thoughts

In this article, we will answer some frequently asked questions about evaluating algebraic expressions.

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that consists of variables, constants, and mathematical operations. It is a way to represent a value or a relationship between values using mathematical symbols.

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

A: To evaluate an algebraic expression, you need to follow these steps:

  1. Substitute the given values into the expression.
  2. Simplify the expression by following the order of operations (PEMDAS).
  3. Perform the arithmetic operations in the correct order.

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

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when simplifying an expression. The acronym 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 handle negative numbers in algebraic expressions?

A: When working with negative numbers in algebraic expressions, you need to follow the rules of arithmetic. For example, when multiplying two negative numbers, the result is positive. When dividing two negative numbers, the result is positive.

Q: Can I use variables with exponents in algebraic expressions?

A: Yes, you can use variables with exponents in algebraic expressions. For example, the expression 2x^2 + 3x - 4 is a valid algebraic expression.

Q: How do I simplify expressions with fractions?

A: To simplify expressions with fractions, you need to follow these steps:

  1. Simplify the numerator and denominator separately.
  2. Cancel out any common factors between the numerator and denominator.
  3. Simplify the resulting fraction.

Q: Can I use algebraic expressions to solve real-world problems?

A: Yes, algebraic expressions can be used to solve real-world problems. For example, you can use algebraic expressions to calculate the cost of goods and services, determine the area and perimeter of shapes, and solve problems in physics and engineering.

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

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

  • Not following the order of operations (PEMDAS)
  • Not substituting the given values into the expression
  • Not simplifying the expression correctly
  • Not handling negative numbers correctly
  • Not using variables with exponents correctly

Q: How can I practice evaluating algebraic expressions?

A: You can practice evaluating algebraic expressions by:

  • Working through example problems in your textbook or online resources
  • Creating your own algebraic expressions and simplifying them
  • Using online tools or calculators to evaluate expressions
  • Practicing with real-world problems and applications

Conclusion

Evaluating algebraic expressions is a fundamental concept in mathematics that has numerous applications in various fields. By understanding how to evaluate algebraic expressions, you can solve problems, make informed decisions, and achieve your goals. Remember to follow the order of operations (PEMDAS), handle negative numbers correctly, and use variables with exponents correctly. With practice and patience, you can become proficient in evaluating algebraic expressions.