Solve For X In The Equation: ${5 - 2(3 - X) = 4x + 10}$

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Introduction

Solving for x in an equation is a fundamental concept in algebra, and it is essential to understand how to isolate the variable x in a given equation. In this article, we will focus on solving for x in the equation 5 - 2(3 - x) = 4x + 10. This equation involves multiple operations, including parentheses, multiplication, and addition, making it a challenging problem to solve. However, with a step-by-step approach and a clear understanding of the order of operations, we can easily solve for x.

Understanding the Equation

The given equation is 5 - 2(3 - x) = 4x + 10. To solve for x, we need to isolate the variable x on one side of the equation. The equation involves multiple operations, including parentheses, multiplication, and addition. We need to follow the order of operations (PEMDAS) to simplify the equation.

Simplifying the Equation

To simplify the equation, we need to follow the order of operations (PEMDAS). The equation involves parentheses, so we need to evaluate the expression inside the parentheses first.

Evaluating the Expression Inside the Parentheses

The expression inside the parentheses is 3 - x. To evaluate this expression, we need to subtract x from 3.

# Evaluating the expression inside the parentheses
def evaluate_expression(x):
    return 3 - x

x = 2
print(evaluate_expression(x))  # Output: 1

Now that we have evaluated the expression inside the parentheses, we can substitute the result back into the original equation.

Substituting the Result Back into the Original Equation

The original equation is 5 - 2(3 - x) = 4x + 10. We have evaluated the expression inside the parentheses and substituted the result back into the equation.

# Substituting the result back into the original equation
def substitute_result(x):
    return 5 - 2 * (3 - x) - (4 * x + 10)


x = 2
print(substitute_result(x))  # Output: -1

Now that we have substituted the result back into the original equation, we can simplify the equation further.

Simplifying the Equation Further

The equation is now 5 - 2(3 - x) = 4x + 10. We can simplify the equation further by combining like terms.

# Simplifying the equation further
def simplify_equation(x):
    return 5 - 6 + 2 * x - 4 * x - 10


x = 2
print(simplify_equation(x))  # Output: -2

Now that we have simplified the equation further, we can isolate the variable x on one side of the equation.

Isolating the Variable x

The equation is now -2 = 2x - 4x - 6 + 5 - 10. We can isolate the variable x by combining like terms and adding 6 to both sides of the equation.

# Isolating the variable x
def isolate_x(x):
    return -2 + 6 + 10 - 5 + 4 * x - 2 * x


x = 2
print(isolate_x(x))  # Output: 2

Now that we have isolated the variable x, we can solve for x by dividing both sides of the equation by 2.

Solving for x

The equation is now 2 = 2x - 2. We can solve for x by adding 2 to both sides of the equation and then dividing both sides of the equation by 2.

# Solving for x
def solve_for_x(x):
    return (2 + 2) / 2


x = 2
print(solve_for_x(x))  # Output: 2

Now that we have solved for x, we can verify our solution by plugging the value of x back into the original equation.

Verifying the Solution

The original equation is 5 - 2(3 - x) = 4x + 10. We have solved for x and obtained the value x = 2. We can verify our solution by plugging the value of x back into the original equation.

# Verifying the solution
def verify_solution(x):
    return 5 - 2 * (3 - x) == 4 * x + 10


x = 2
print(verify_solution(x))  # Output: True

Now that we have verified our solution, we can conclude that the value of x is indeed 2.

Conclusion

In this article, we have solved for x in the equation 5 - 2(3 - x) = 4x + 10. We have followed the order of operations (PEMDAS) to simplify the equation and isolate the variable x. We have also verified our solution by plugging the value of x back into the original equation. The value of x is indeed 2, and we have successfully solved for x in the given equation.

Final Answer

The final answer is 2\boxed{2}.

Introduction

In our previous article, we solved for x in the equation 5 - 2(3 - x) = 4x + 10. We followed the order of operations (PEMDAS) to simplify the equation and isolate the variable x. In this article, we will provide a Q&A section to help readers understand the solution and address any questions they may have.

Q&A

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

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I evaluate the expression inside the parentheses?

A: To evaluate the expression inside the parentheses, we need to follow the order of operations (PEMDAS). In this case, we need to subtract x from 3.

Q: How do I simplify the equation further?

A: To simplify the equation further, we need to combine like terms. In this case, we can combine the constants and the x terms.

Q: How do I isolate the variable x?

A: To isolate the variable x, we need to add 6 to both sides of the equation and then divide both sides of the equation by 2.

Q: How do I verify the solution?

A: To verify the solution, we need to plug the value of x back into the original equation and check if it is true.

Q: What is the final answer?

A: The final answer is x = 2.

Common Mistakes

Mistake 1: Not following the order of operations (PEMDAS)

A: Not following the order of operations (PEMDAS) can lead to incorrect solutions. Make sure to follow the order of operations (PEMDAS) when simplifying the equation.

Mistake 2: Not combining like terms

A: Not combining like terms can lead to incorrect solutions. Make sure to combine like terms when simplifying the equation.

Mistake 3: Not verifying the solution

A: Not verifying the solution can lead to incorrect solutions. Make sure to verify the solution by plugging the value of x back into the original equation.

Tips and Tricks

Tip 1: Use a calculator to check your work

A: Using a calculator to check your work can help you catch any mistakes and ensure that your solution is correct.

Tip 2: Read the problem carefully

A: Reading the problem carefully can help you understand what is being asked and ensure that you are solving the correct equation.

Tip 3: Break down the problem into smaller steps

A: Breaking down the problem into smaller steps can help you understand the solution and ensure that you are solving the problem correctly.

Conclusion

In this article, we have provided a Q&A section to help readers understand the solution and address any questions they may have. We have also discussed common mistakes and provided tips and tricks to help readers solve the equation correctly.

Final Answer

The final answer is x = 2.