Which Equation Can Be Used To Find The Value Of $x$? 168 = 18 ⋅ X + 12 ⋅ 2 X 168 = 18 \cdot X + 12 \cdot 2x 168 = 18 ⋅ X + 12 ⋅ 2 X What Is The Value Of $x$? X = □ X = \square X = □
Introduction
Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will explore how to solve a linear equation, specifically the equation $168 = 18 \cdot x + 12 \cdot 2x$. We will break down the steps involved in solving this equation and provide a clear explanation of the process.
Understanding the Equation
The given equation is $168 = 18 \cdot x + 12 \cdot 2x$. To solve for $x$, we need to isolate the variable $x$ on one side of the equation. The first step is to simplify the equation by combining like terms.
Simplifying the Equation
The equation can be simplified by combining the terms involving $x$. We can rewrite the equation as:
Now, we can combine the like terms:
Isolating the Variable
To isolate the variable $x$, we need to get rid of the coefficient $42$. We can do this by dividing both sides of the equation by $42$.
This simplifies to:
Verifying the Solution
To verify the solution, we can plug the value of $x$ back into the original equation and check if it is true.
Simplifying the equation, we get:
This simplifies to:
Since the equation is true, we can confirm that the value of $x$ is indeed $4$.
Conclusion
Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, we can solve the equation $168 = 18 \cdot x + 12 \cdot 2x$ and find the value of $x$. The key steps involved in solving this equation are simplifying the equation, isolating the variable, and verifying the solution. By practicing these steps, students can become proficient in solving linear equations and apply this skill to a wide range of mathematical problems.
Tips and Tricks
- When solving linear equations, it's essential to simplify the equation by combining like terms.
- To isolate the variable, divide both sides of the equation by the coefficient.
- Verify the solution by plugging the value of the variable back into the original equation.
Common Mistakes to Avoid
- Failing to simplify the equation by combining like terms.
- Not isolating the variable by dividing both sides of the equation by the coefficient.
- Not verifying the solution by plugging the value of the variable back into the original equation.
Real-World Applications
Solving linear equations has numerous real-world applications. For example:
- In finance, linear equations are used to calculate interest rates and investment returns.
- In physics, linear equations are used to describe the motion of objects and calculate forces.
- In engineering, linear equations are used to design and optimize systems.
Practice Problems
- Solve the equation $24 = 4 \cdot x + 6 \cdot 2x$.
- Solve the equation $36 = 9 \cdot x + 12 \cdot 3x$.
- Solve the equation $48 = 8 \cdot x + 16 \cdot 2x$.
Answer Key
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x = 2$<br/>
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable(s) is 1. It is a simple equation that can be solved by using basic algebraic operations.
Q: How do I simplify a linear equation?
A: To simplify a linear equation, combine like terms by adding or subtracting the coefficients of the same variable. For example, in the equation $2x + 3x = 5x$, the like terms are $2x$ and $3x$, which can be combined to get $5x$.
Q: How do I isolate the variable in a linear equation?
A: To isolate the variable in a linear equation, divide both sides of the equation by the coefficient of the variable. For example, in the equation $4x = 12$, divide both sides by 4 to get $x = 3$.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, the equation $x + 2 = 5$ is a linear equation, while the equation $x^2 + 2x + 1 = 0$ is a quadratic equation.
Q: How do I solve a linear equation with fractions?
A: To solve a linear equation with fractions, multiply both sides of the equation by the least common multiple (LCM) of the denominators. For example, in the equation $\frac{1}{2}x = 3$, multiply both sides by 2 to get $x = 6$.
Q: Can I use a calculator to solve a linear equation?
A: Yes, you can use a calculator to solve a linear equation. However, it's essential to understand the steps involved in solving the equation and to verify the solution by plugging the value of the variable back into the original equation.
Q: What are some common mistakes to avoid when solving linear equations?
A: Some common mistakes to avoid when solving linear equations include:
- Failing to simplify the equation by combining like terms.
- Not isolating the variable by dividing both sides of the equation by the coefficient.
- Not verifying the solution by plugging the value of the variable back into the original equation.
Q: How do I apply linear equations to real-world problems?
A: Linear equations can be applied to a wide range of real-world problems, including:
- Finance: calculating interest rates and investment returns.
- Physics: describing the motion of objects and calculating forces.
- Engineering: designing and optimizing systems.
Q: Can I use linear equations to solve systems of equations?
A: Yes, you can use linear equations to solve systems of equations. A system of equations is a set of two or more linear equations that are solved simultaneously. To solve a system of equations, use substitution or elimination methods to find the values of the variables.
Q: What are some advanced topics in linear equations?
A: Some advanced topics in linear equations include:
- Systems of linear equations.
- Linear inequalities.
- Matrices and determinants.
- Linear programming.
Conclusion
Solving linear equations is a fundamental skill in mathematics, and it has numerous real-world applications. By understanding the steps involved in solving linear equations and avoiding common mistakes, you can become proficient in solving linear equations and apply this skill to a wide range of mathematical problems.