Evaluate The Expression For $m = -3$.$-4|5+m|$Type The Correct Answer In The Box. Use Numerals.The Value Of The Expression Is $\square$.

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Understanding the Problem

When evaluating the expression $-4|5+m|$, we need to substitute the value of $m$ into the expression and then simplify it. In this case, we are given that $m = -3$. Our goal is to find the value of the expression when $m$ is equal to $-3$.

Substituting the Value of $m$

To substitute the value of $m$ into the expression, we need to replace $m$ with $-3$ in the expression $-4|5+m|$. This gives us:

$$-4|5+(-3)|$$

Simplifying the Expression

Now that we have substituted the value of $m$, we can simplify the expression. The first step is to evaluate the expression inside the absolute value signs. We have:

$$|5+(-3)| = |2|$$

Since the absolute value of a number is always non-negative, we can simplify this expression as:

$$|2| = 2$$

Evaluating the Final Expression

Now that we have simplified the expression inside the absolute value signs, we can evaluate the final expression. We have:

$$-4|2| = -4(2)$$

Calculating the Final Answer

To calculate the final answer, we need to multiply $-4$ by $2$. This gives us:

$$-4(2) = -8$$

Conclusion

In conclusion, when we substitute $m = -3$ into the expression $-4|5+m|$, we get:

$$-4|5+(-3)| = -4|2| = -8$$

Therefore, the value of the expression is $\boxed{-8}$.

Step-by-Step Solution

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

1. Substitute $m = -3$ into the expression $-4|5+m|$.
2. Simplify the expression inside the absolute value signs.
3. Evaluate the final expression.
4. Calculate the final answer.

Common Mistakes

Here are some common mistakes to avoid when solving this problem:

• Not substituting the value of $m$ into the expression.
• Not simplifying the expression inside the absolute value signs.
• Not evaluating the final expression correctly.
• Not calculating the final answer correctly.

Tips and Tricks

Here are some tips and tricks to help you solve this problem:

• Make sure to substitute the value of $m$ into the expression correctly.
• Simplify the expression inside the absolute value signs carefully.
• Evaluate the final expression step by step.
• Calculate the final answer carefully.

Real-World Applications

This problem has real-world applications in mathematics and science. For example, in physics, the absolute value of a quantity can represent the magnitude of a force or a velocity. In engineering, the absolute value of a quantity can represent the magnitude of a signal or a noise.

Conclusion

In conclusion, evaluating the expression $-4|5+m|$ for $m = -3$ requires careful substitution, simplification, and evaluation of the expression. By following the step-by-step solution and avoiding common mistakes, you can arrive at the correct answer of $\boxed{-8}$. This problem has real-world applications in mathematics and science, and it requires careful attention to detail and a solid understanding of absolute value and algebraic expressions.

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Frequently Asked Questions

Q: What is the value of the expression $-4|5+m|$ when $m = -3$?

A: The value of the expression $-4|5+m|$ when $m = -3$ is $\boxed{-8}$.

Q: How do I substitute the value of $m$ into the expression?

A: To substitute the value of $m$ into the expression, you need to replace $m$ with $-3$ in the expression $-4|5+m|$.

Q: What is the first step in simplifying the expression?

A: The first step in simplifying the expression is to evaluate the expression inside the absolute value signs.

Q: How do I evaluate the expression inside the absolute value signs?

A: To evaluate the expression inside the absolute value signs, you need to add $5$ and $-3$ together.

Q: What is the result of adding $5$ and $-3$ together?

A: The result of adding $5$ and $-3$ together is $2$.

Q: What is the next step in simplifying the expression?

A: The next step in simplifying the expression is to multiply $-4$ by the result of the expression inside the absolute value signs.

Q: What is the result of multiplying $-4$ by $2$?

A: The result of multiplying $-4$ by $2$ is $-8$.

Q: What is the final answer to the problem?

A: The final answer to the problem is $\boxed{-8}$.

Q: What are some common mistakes to avoid when solving this problem?

A: Some common mistakes to avoid when solving this problem include not substituting the value of $m$ into the expression, not simplifying the expression inside the absolute value signs, and not evaluating the final expression correctly.

Q: What are some tips and tricks to help me solve this problem?

A: Some tips and tricks to help you solve this problem include making sure to substitute the value of $m$ into the expression correctly, simplifying the expression inside the absolute value signs carefully, and evaluating the final expression step by step.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in mathematics and science, such as representing the magnitude of a force or a velocity in physics, or representing the magnitude of a signal or a noise in engineering.

Additional Resources

• For more information on absolute value and algebraic expressions, see the following resources:

• Khan Academy: Absolute Value
• Mathway: Absolute Value
• Wolfram Alpha: Absolute Value

• For more information on real-world applications of this problem, see the following resources:

• Physics Classroom: Absolute Value
• Engineering Toolbox: Absolute Value
• Math Open Reference: Absolute Value

Conclusion

In conclusion, evaluating the expression $-4|5+m|$ for $m = -3$ requires careful substitution, simplification, and evaluation of the expression. By following the step-by-step solution and avoiding common mistakes, you can arrive at the correct answer of $\boxed{-8}$. This problem has real-world applications in mathematics and science, and it requires careful attention to detail and a solid understanding of absolute value and algebraic expressions.