What Is The Solution To This Equation?${ \frac{x}{4} = -12 }$A. { X = 48$}$ B. { X = -48$}$ C. { X = -3$}$ D. { X = 3$}$

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Introduction

In mathematics, solving equations is a fundamental concept that helps us find the value of unknown variables. Equations are statements that express the equality of two mathematical expressions, and solving them involves isolating the variable on one side of the equation. In this article, we will focus on solving a simple equation involving fractions, and we will explore the step-by-step process to find the solution.

Understanding the Equation

The given equation is x4=−12\frac{x}{4} = -12. This equation states that the quotient of xx and 44 is equal to −12-12. To solve for xx, we need to isolate the variable on one side of the equation.

Step 1: Multiply Both Sides by 4

To eliminate the fraction, we can multiply both sides of the equation by 44. This will help us get rid of the denominator and isolate the variable.

x4×4=−12×4\frac{x}{4} \times 4 = -12 \times 4

Step 2: Simplify the Equation

After multiplying both sides by 44, we get:

x=−48x = -48

Step 3: Check the Solution

To verify that our solution is correct, we can plug it back into the original equation and check if it satisfies the equation.

−484=−12\frac{-48}{4} = -12

Conclusion

By following the step-by-step process, we have successfully solved the equation x4=−12\frac{x}{4} = -12. The solution to this equation is x=−48x = -48. This means that when we divide −48-48 by 44, we get −12-12, which satisfies the original equation.

Why is this Solution Correct?

The solution x=−48x = -48 is correct because it satisfies the original equation. When we substitute x=−48x = -48 into the equation, we get:

−484=−12\frac{-48}{4} = -12

This shows that the solution x=−48x = -48 is indeed correct.

What if the Solution is Not Correct?

If the solution is not correct, it means that the equation has no solution or that the solution is not unique. In this case, we need to re-examine the equation and the steps we took to solve it.

Common Mistakes to Avoid

When solving equations, there are several common mistakes to avoid. These include:

  • Not following the order of operations: When solving equations, it's essential to follow the order of operations (PEMDAS) to ensure that we perform the operations in the correct order.
  • Not checking the solution: Before accepting a solution, it's crucial to check it by plugging it back into the original equation.
  • Not considering multiple solutions: Some equations may have multiple solutions, so it's essential to consider all possible solutions.

Real-World Applications

Solving equations has numerous real-world applications. For example:

  • Physics and Engineering: Equations are used to describe the laws of physics and engineering, and solving them helps us understand the behavior of physical systems.
  • Computer Science: Equations are used in computer science to model complex systems and solve problems.
  • Economics: Equations are used in economics to model economic systems and make predictions about economic behavior.

Conclusion

In conclusion, solving equations is a fundamental concept in mathematics that helps us find the value of unknown variables. By following the step-by-step process and avoiding common mistakes, we can successfully solve equations and apply them to real-world problems.

Final Answer

The final answer to the equation x4=−12\frac{x}{4} = -12 is x=−48x = -48.

Introduction

Solving equations is a fundamental concept in mathematics that helps us find the value of unknown variables. In this article, we will address some frequently asked questions (FAQs) about solving equations, providing a deeper understanding of the concept and its applications.

Q: What is an equation?

A: An equation is a statement that expresses the equality of two mathematical expressions. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), which are separated by an equal sign (=).

Q: What is the order of operations?

A: The order of operations (PEMDAS) is a set of rules that dictates the order in which we perform mathematical operations. The acronym PEMDAS stands for:

  • Parentheses: Evaluate expressions inside parentheses first.
  • Exponents: Evaluate any exponential expressions next.
  • Multiplication and Division: Evaluate multiplication and division operations from left to right.
  • Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I solve a linear equation?

A: To solve a linear equation, follow these steps:

  1. Simplify the equation by combining like terms.
  2. Isolate the variable on one side of the equation.
  3. Use inverse operations to eliminate any coefficients or constants.
  4. Check the solution by plugging it back into the original equation.

Q: What is a quadratic equation?

A: A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. It has the general form:

ax^2 + bx + c = 0

where a, b, and c are constants, and x is the variable.

Q: How do I solve a quadratic equation?

A: To solve a quadratic equation, you can use the following methods:

  1. Factoring: If the quadratic expression can be factored into the product of two binomials, you can set each factor equal to zero and solve for the variable.
  2. Quadratic Formula: The quadratic formula is a formula that gives the solutions to a quadratic equation. It is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

Q: What is a system of equations?

A: A system of equations is a set of two or more equations that are solved simultaneously. Each equation in the system is called an equation, and the solution to the system is the set of values that satisfy all the equations.

Q: How do I solve a system of equations?

A: To solve a system of equations, you can use the following methods:

  1. Substitution Method: Substitute the expression for one variable from one equation into the other equation.
  2. Elimination Method: Add or subtract the equations to eliminate one of the variables.
  3. Graphical Method: Graph the equations on a coordinate plane and find the point of intersection.

Q: What is a linear inequality?

A: A linear inequality is an inequality that involves a linear expression. It has the general form:

ax + b > c

or

ax + b < c

where a, b, and c are constants, and x is the variable.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, follow these steps:

  1. Simplify the inequality by combining like terms.
  2. Isolate the variable on one side of the inequality.
  3. Use inverse operations to eliminate any coefficients or constants.
  4. Check the solution by plugging it back into the original inequality.

Conclusion

Solving equations is a fundamental concept in mathematics that helps us find the value of unknown variables. By understanding the basics of equations and practicing solving them, you can develop problem-solving skills and apply them to real-world problems.

Final Answer

The final answer to the FAQs about solving equations is that it is a fundamental concept in mathematics that helps us find the value of unknown variables. By following the step-by-step process and using the correct methods, we can successfully solve equations and apply them to real-world problems.