Evaluate The Expression 4 Y + 2 Y − 3 4y + 2y - 3 4 Y + 2 Y − 3 When Y = − 5 Y = -5 Y = − 5 .

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Introduction

In algebra, evaluating an expression involves substituting a given value for a variable and simplifying the resulting expression. In this article, we will evaluate the expression $4y + 2y - 3$ when $y = -5$. This will involve substituting $y = -5$ into the expression and simplifying the resulting expression.

Understanding the Expression

The given expression is $4y + 2y - 3$. This expression involves two variables, $y$, and a constant, $-3$. The expression can be simplified by combining like terms. Like terms are terms that have the same variable raised to the same power.

Simplifying the Expression

To simplify the expression, we can combine the like terms. The like terms in the expression are $4y$ and $2y$. These terms can be combined by adding their coefficients. The coefficient of $4y$ is $4$ and the coefficient of $2y$ is $2$. Adding these coefficients gives us $6y$.

Evaluating the Expression

Now that we have simplified the expression to $6y - 3$, we can substitute $y = -5$ into the expression. Substituting $y = -5$ gives us $6(-5) - 3$.

Simplifying the Resulting Expression

To simplify the resulting expression, we can evaluate the expression $6(-5) - 3$. The expression $6(-5)$ can be evaluated by multiplying $6$ and $-5$. This gives us $-30$. Now we can substitute this value into the expression $-30 - 3$.

Final Answer

Evaluating the expression $-30 - 3$ gives us $-33$. Therefore, the value of the expression $4y + 2y - 3$ when $y = -5$ is $-33$.

Conclusion

In this article, we evaluated the expression $4y + 2y - 3$ when $y = -5$. We simplified the expression by combining like terms and then substituted $y = -5$ into the expression. Finally, we evaluated the resulting expression to get the final answer of $-33$.

Step-by-Step Solution

Here is a step-by-step solution to the problem:

1. Simplify the expression $4y + 2y - 3$ by combining like terms.
2. Substitute $y = -5$ into the simplified expression.
3. Evaluate the resulting expression to get the final answer.

Tips and Tricks

• When simplifying an expression, make sure to combine like terms.
• When substituting a value into an expression, make sure to substitute the value for the variable.
• When evaluating an expression, make sure to follow the order of operations (PEMDAS).

Frequently Asked Questions

• Q: What is the value of the expression $4y + 2y - 3$ when $y = -5$? A: The value of the expression $4y + 2y - 3$ when $y = -5$ is $-33$.
• Q: How do I simplify an expression? A: To simplify an expression, combine like terms.
• Q: How do I substitute a value into an expression? A: To substitute a value into an expression, substitute the value for the variable.

Related Topics

• Evaluating expressions
• Simplifying expressions
• Substituting values into expressions

References

• [1] Algebra for Dummies, by Mary Jane Sterling
• [2] Calculus for Dummies, by Mark Ryan
• [3] Math for Life, by Michael Sullivan
  

Introduction

Evaluating expressions is a fundamental concept in algebra that involves substituting a given value for a variable and simplifying the resulting expression. In this article, we will provide a Q&A guide to help you understand how to evaluate expressions and answer common questions related to this topic.

Q: What is an expression in algebra?

A: An expression in algebra is a combination of variables, constants, and mathematical operations. It can be a simple expression, such as $2x + 3$, or a more complex expression, such as $4x^2 + 2x - 3$.

Q: How do I evaluate an expression?

A: To evaluate an expression, you need to substitute a given value for the variable and simplify the resulting expression. For example, if you have the expression $2x + 3$ and you want to evaluate it when $x = 4$, you would substitute $x = 4$ into the expression and simplify it to get $2(4) + 3 = 11$.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first 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 simplify an expression?

A: To simplify an expression, you need to combine like terms. Like terms are terms that have the same variable raised to the same power. For example, if you have the expression $2x + 3x$, you can combine the like terms to get $5x$.

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

A: An expression is a combination of variables, constants, and mathematical operations, while an equation is a statement that says two expressions are equal. For example, $2x + 3 = 5$ is an equation, while $2x + 3$ is an expression.

Q: How do I evaluate an expression with fractions?

A: To evaluate an expression with fractions, you need to follow the order of operations and simplify the expression. For example, if you have the expression $\frac{2x}{3} + \frac{1}{2}$ and you want to evaluate it when $x = 4$, you would substitute $x = 4$ into the expression and simplify it to get $\frac{2(4)}{3} + \frac{1}{2} = \frac{8}{3} + \frac{1}{2}$.

Q: How do I evaluate an expression with decimals?

A: To evaluate an expression with decimals, you need to follow the order of operations and simplify the expression. For example, if you have the expression $2.5x + 3.2$ and you want to evaluate it when $x = 4$, you would substitute $x = 4$ into the expression and simplify it to get $2.5(4) + 3.2 = 10 + 3.2 = 13.2$.

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
• Not simplifying the expression
• Not combining like terms
• Not substituting the correct value for the variable

Q: How can I practice evaluating expressions?

A: You can practice evaluating expressions by working through problems in a textbook or online resource. You can also try creating your own expressions and evaluating them to see if you can get the correct answer.

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

A: Evaluating expressions has many real-world applications, including:

• Science: Evaluating expressions is used to model real-world phenomena, such as the motion of objects or the growth of populations.
• Engineering: Evaluating expressions is used to design and optimize systems, such as bridges or electronic circuits.
• Finance: Evaluating expressions is used to calculate interest rates and investment returns.

Conclusion

Evaluating expressions is a fundamental concept in algebra that involves substituting a given value for a variable and simplifying the resulting expression. By following the order of operations and simplifying the expression, you can evaluate expressions and solve problems in a variety of fields.