Solve For \[$ X \$\]:$\[ 4 \times 17 \left( \frac{83}{-4} \right) = X \\]

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Introduction to the Problem

When solving for $x$ in the given equation, we need to follow the order of operations (PEMDAS) to simplify the expression and isolate the variable. The equation involves multiplication, division, and exponentiation, which we will address step by step.

Understanding the Order of Operations

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS stands for:

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.

Breaking Down the Equation

The given equation is $4 \times 17 \left( \frac{83}{-4} \right) = x$. To solve for $x$, we need to simplify the expression inside the parentheses first.

Simplifying the Fraction

The fraction $\frac{83}{-4}$ can be simplified by dividing the numerator by the denominator. However, since the denominator is negative, the sign of the result will be positive.

$\frac{83}{-4} = -\frac{83}{4}$

Multiplying the Numerator and Denominator

Now that we have simplified the fraction, we can multiply the numerator and denominator by $-1$ to get rid of the negative sign.

$-\frac{83}{4} = \frac{83}{-4} = \frac{-83}{4}$

Multiplying the Expression by 4 and 17

Now that we have simplified the fraction, we can multiply the expression by 4 and 17.

$4 \times 17 \left( \frac{-83}{4} \right) = 4 \times 17 \times \frac{-83}{4}$

Canceling Out the Common Factor

We can cancel out the common factor of 4 in the numerator and denominator.

$4 \times 17 \times \frac{-83}{4} = 17 \times \frac{-83}{1}$

Multiplying the Numerator and Denominator

Now that we have canceled out the common factor, we can multiply the numerator and denominator.

$17 \times \frac{-83}{1} = -\frac{1406}{1}$

Simplifying the Expression

The expression $-\frac{1406}{1}$ can be simplified by removing the fraction.

$-\frac{1406}{1} = -1406$

Conclusion

In conclusion, to solve for $x$ in the given equation, we need to follow the order of operations and simplify the expression inside the parentheses first. We can then multiply the expression by 4 and 17, cancel out the common factor, and finally simplify the expression to get the value of $x$.

Final Answer

The final answer is $\boxed{-1406}$.

Step-by-Step Solution

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

1. Simplify the fraction $\frac{83}{-4}$ to get $-\frac{83}{4}$.
2. Multiply the expression by 4 and 17 to get $4 \times 17 \left( \frac{-83}{4} \right)$.
3. Cancel out the common factor of 4 in the numerator and denominator to get $17 \times \frac{-83}{1}$.
4. Multiply the numerator and denominator to get $-\frac{1406}{1}$.
5. Simplify the expression to get $-1406$.

Frequently Asked Questions

• Q: What is the order of operations? A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression.
• Q: How do I simplify a fraction? A: To simplify a fraction, you can divide the numerator by the denominator.
• Q: How do I multiply an expression by a number? A: To multiply an expression by a number, you can multiply each term in the expression by the number.
• Q: How do I cancel out a common factor? A: To cancel out a common factor, you can divide each term in the expression by the common factor.

Related Topics

• Simplifying fractions
• Multiplying expressions
• Canceling out common factors
• Order of operations

References

• [1] Khan Academy. (n.d.). Order of Operations. Retrieved from https://www.khanacademy.org/math/algebra/x2f6b7f/x2f6b7f/x2f6b7f
• [2] Mathway. (n.d.). Order of Operations. Retrieved from https://www.mathway.com/subjects/Order-of-Operations
• [3] Purplemath. (n.d.). Order of Operations. Retrieved from https://www.purplemath.com/modules/orderofop.htm
  

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Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS stands for:

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: How do I simplify a fraction?

A: To simplify a fraction, you can divide the numerator by the denominator. For example, to simplify the fraction $\frac{83}{-4}$, you can divide the numerator by the denominator to get $-\frac{83}{4}$.

Q: How do I multiply an expression by a number?

A: To multiply an expression by a number, you can multiply each term in the expression by the number. For example, to multiply the expression $4 \times 17 \left( \frac{-83}{4} \right)$ by 4, you can multiply each term in the expression by 4 to get $4 \times 17 \times \frac{-83}{4}$.

Q: How do I cancel out a common factor?

A: To cancel out a common factor, you can divide each term in the expression by the common factor. For example, to cancel out the common factor of 4 in the expression $4 \times 17 \times \frac{-83}{4}$, you can divide each term in the expression by 4 to get $17 \times \frac{-83}{1}$.

Q: What is the final answer to the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: The final answer to the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$ is $-1406$.

Q: How do I know which operation to perform first when there are multiple operations in an expression?

A: To determine which operation to perform first, you can use the order of operations (PEMDAS). Evaluate expressions inside parentheses first, then evaluate any exponential expressions, followed by multiplication and division operations from left to right, and finally evaluate any addition and subtraction operations from left to right.

Q: Can I use a calculator to solve the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: Yes, you can use a calculator to solve the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$. However, it's also important to understand the steps involved in solving the equation and to be able to explain the solution.

Q: How do I check my answer to the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: To check your answer, you can plug the value of $x$ back into the original equation and simplify the expression. If the expression simplifies to the original equation, then your answer is correct.

Q: Can I use a different method to solve the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: Yes, you can use a different method to solve the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$. For example, you can use algebraic manipulation or numerical methods to solve the equation.

Q: How do I know if my solution to the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$ is correct?

A: To determine if your solution is correct, you can check your answer by plugging the value of $x$ back into the original equation and simplifying the expression. If the expression simplifies to the original equation, then your answer is correct.

Q: Can I use a graphing calculator to solve the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: Yes, you can use a graphing calculator to solve the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$. However, it's also important to understand the steps involved in solving the equation and to be able to explain the solution.

Q: How do I know if my graphing calculator is set up correctly to solve the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: To determine if your graphing calculator is set up correctly, you can check the settings and make sure that the calculator is in the correct mode. You can also use the calculator's built-in functions to check the solution.

Q: Can I use a computer program to solve the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: Yes, you can use a computer program to solve the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$. However, it's also important to understand the steps involved in solving the equation and to be able to explain the solution.

Q: How do I know if my computer program is set up correctly to solve the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: To determine if your computer program is set up correctly, you can check the code and make sure that the program is in the correct mode. You can also use the program's built-in functions to check the solution.

Q: Can I use a spreadsheet to solve the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: Yes, you can use a spreadsheet to solve the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$. However, it's also important to understand the steps involved in solving the equation and to be able to explain the solution.

Q: How do I know if my spreadsheet is set up correctly to solve the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: To determine if your spreadsheet is set up correctly, you can check the formulas and make sure that the spreadsheet is in the correct mode. You can also use the spreadsheet's built-in functions to check the solution.

Q: Can I use a calculator to check my answer to the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: Yes, you can use a calculator to check your answer to the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$. Simply plug the value of $x$ back into the original equation and simplify the expression. If the expression simplifies to the original equation, then your answer is correct.

Q: How do I know if my calculator is set up correctly to check my answer to the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: To determine if your calculator is set up correctly, you can check the settings and make sure that the calculator is in the correct mode. You can also use the calculator's built-in functions to check the solution.

Q: Can I use a computer program to check my answer to the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: Yes, you can use a computer program to check your answer to the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$. Simply plug the value of $x$ back into the original equation and simplify the expression. If the expression simplifies to the original equation, then your answer is correct.

Q: How do I know if my computer program is set up correctly to check my answer to the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: To determine if your computer program is set up correctly, you can check the code and make sure that the program is in the correct mode. You can also use the program's built-in functions to check the solution.

Q: Can I use a spreadsheet to check my answer to the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$?

A: Yes, you can use a spreadsheet to check your answer to the equation $4 \times 17 \left( \frac{83}{-4} \right) = x$. Simply plug the value of $x$ back into the original equation and simplify the expression. If the expression simplifies to the original equation, then your answer is correct.

Q: How do I know if my spreadsheet is set up correctly to check my answer to the equation $4 \times 17 \left( \frac{