A. Evaluate $3(x+2y)$ When $x=3$ And \$y=1$[/tex\].b. Is The Number You Obtained In Part (a) A Solution Of $7z-94=13$?

Introduction

In this article, we will evaluate an algebraic expression and determine if the obtained value is a solution to a given linear equation. We will start by evaluating the expression $3(x+2y)$ when $x=3$ and $y=1$. Then, we will check if the obtained value is a solution to the equation $7z-94=13$.

Evaluating the Algebraic Expression

To evaluate the expression $3(x+2y)$, we need to substitute the values of $x$ and $y$ into the expression. We are given that $x=3$ and $y=1$. Substituting these values into the expression, we get:

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

Using the order of operations (PEMDAS), we first evaluate the expression inside the parentheses:

$$3+2(1) = 3+2 = 5$$

Now, we multiply the result by 3:

$$3(5) = 15$$

Therefore, the value of the expression $3(x+2y)$ when $x=3$ and $y=1$ is 15.

Is the Obtained Value a Solution to the Linear Equation?

Now that we have evaluated the expression, we need to check if the obtained value is a solution to the equation $7z-94=13$. To do this, we need to substitute the value of $z$ into the equation and check if the equation is true.

We are given that the value of the expression $3(x+2y)$ when $x=3$ and $y=1$ is 15. We can substitute this value into the equation as follows:

$$7(15)-94=13$$

First, we multiply 7 by 15:

$$7(15) = 105$$

Now, we subtract 94 from the result:

$$105-94 = 11$$

The equation is not true, since 11 is not equal to 13. Therefore, the value of 15 is not a solution to the equation $7z-94=13$.

Conclusion

In this article, we evaluated the algebraic expression $3(x+2y)$ when $x=3$ and $y=1$ and obtained a value of 15. We then checked if this value is a solution to the linear equation $7z-94=13$ and found that it is not.

Key Takeaways

• To evaluate an algebraic expression, we need to substitute the values of the variables into the expression and follow the order of operations.
• To check if a value is a solution to a linear equation, we need to substitute the value into the equation and check if the equation is true.
• If the equation is not true, then the value is not a solution to the equation.

Further Reading

If you want to learn more about evaluating algebraic expressions and solving linear equations, I recommend checking out the following resources:

• Khan Academy: Algebra
• Mathway: Algebra
• Wolfram Alpha: Algebra

References

• [1] "Algebra" by Michael Artin
• [2] "Linear Algebra" by Jim Hefferon
• [3] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton

Glossary

• Algebraic expression: An expression that contains variables and constants, and is used to represent a value or a relationship between values.
• Linear equation: An equation that contains a single variable and is used to represent a relationship between the variable and a constant.
• Solution: A value that satisfies an equation or inequality.
• Order of operations: A set of rules that determines the order in which operations should be performed when evaluating an expression.
  Evaluating Algebraic Expressions and Solving Linear Equations: Q&A ================================================================

Introduction

In our previous article, we evaluated an algebraic expression and determined if the obtained value is a solution to a given linear equation. In this article, we will answer some frequently asked questions (FAQs) related to evaluating algebraic expressions and solving linear equations.

Q&A

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that contains variables and constants, and is used to represent a value or a relationship between values.

Q: What is a linear equation?

A: A linear equation is an equation that contains a single variable and is used to represent a relationship between the variable and a constant.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the values of the variables into the expression and follow the order of operations (PEMDAS).

Q: What is the order of operations?

A: The order of operations is a set of rules that determines the order in which operations should be performed when evaluating an expression. The order of operations is:

1. Parentheses: Evaluate 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: How do I check if a value is a solution to a linear equation?

A: To check if a value is a solution to a linear equation, you need to substitute the value into the equation and check if the equation is true.

Q: What is a solution to a linear equation?

A: A solution to a linear equation is a value that satisfies the equation.

Q: Can a value be a solution to a linear equation if it is not an integer?

A: Yes, a value can be a solution to a linear equation even if it is not an integer. For example, the value 3.5 is a solution to the equation 2x = 7.

Q: How do I solve a linear equation with multiple variables?

A: To solve a linear equation with multiple variables, you need to isolate one of the variables and then substitute the value into the other equation.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation that contains a single variable and is used to represent a relationship between the variable and a constant. A quadratic equation is an equation that contains a squared variable and is used to represent a relationship between the variable and a constant.

Q: Can a linear equation have multiple solutions?

A: Yes, a linear equation can have multiple solutions. For example, the equation x + 2 = 4 has two solutions: x = 2 and x = 6.

Conclusion

In this article, we answered some frequently asked questions related to evaluating algebraic expressions and solving linear equations. We hope that this article has been helpful in clarifying any confusion you may have had about these topics.

Key Takeaways

• An algebraic expression is a mathematical expression that contains variables and constants.
• A linear equation is an equation that contains a single variable and is used to represent a relationship between the variable and a constant.
• To evaluate an algebraic expression, you need to substitute the values of the variables into the expression and follow the order of operations.
• To check if a value is a solution to a linear equation, you need to substitute the value into the equation and check if the equation is true.
• A solution to a linear equation is a value that satisfies the equation.

Further Reading

If you want to learn more about evaluating algebraic expressions and solving linear equations, I recommend checking out the following resources:

• Khan Academy: Algebra
• Mathway: Algebra
• Wolfram Alpha: Algebra

References

• [1] "Algebra" by Michael Artin
• [2] "Linear Algebra" by Jim Hefferon
• [3] "Mathematics for Computer Science" by Eric Lehman and Tom Leighton

Glossary

• Algebraic expression: A mathematical expression that contains variables and constants.
• Linear equation: An equation that contains a single variable and is used to represent a relationship between the variable and a constant.
• Solution: A value that satisfies an equation or inequality.
• Order of operations: A set of rules that determines the order in which operations should be performed when evaluating an expression.