Solve The Equation And Check The Solution.$\[ 2x - 10 = 18 \\]$\[ X = \square \\] (Simplify Your Answer.)
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 focus on solving a simple linear equation and checking the solution. We will use the equation 2x - 10 = 18 as an example.
What is a Linear Equation?
A linear equation is an equation in which the highest power of the variable (in this case, x) is 1. It can be written in the form ax + b = c, where a, b, and c are constants. Linear equations can be solved using various methods, including addition, subtraction, multiplication, and division.
The Equation to be Solved
The equation we will be solving is 2x - 10 = 18. This is a linear equation in one variable, x.
Step 1: Add 10 to Both Sides
To solve the equation, we need to isolate the variable x. The first step is to add 10 to both sides of the equation. This will eliminate the negative term and make it easier to solve for x.
Step 2: Divide Both Sides by 2
Now that we have 2x = 28, we need to isolate x by dividing both sides of the equation by 2.
Checking the Solution
To check the solution, we need to plug x = 14 back into the original equation and see if it is true.
Since the equation is true, we can conclude that x = 14 is the solution to the equation 2x - 10 = 18.
Conclusion
Solving linear equations is an essential skill for students to master. By following the steps outlined in this article, we can solve simple linear equations like 2x - 10 = 18. Remember to always check the solution by plugging it back into the original equation.
Common Mistakes to Avoid
When solving linear equations, there are several common mistakes to avoid. These include:
- Not isolating the variable: Make sure to isolate the variable x by adding, subtracting, multiplying, or dividing both sides of the equation.
- Not checking the solution: Always check the solution by plugging it back into the original equation.
- Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when solving the equation.
Real-World Applications
Linear equations have many real-world applications. Some examples include:
- Finance: Linear equations can be used to calculate interest rates, investment returns, and other financial metrics.
- Science: Linear equations can be used to model population growth, chemical reactions, and other scientific phenomena.
- Engineering: Linear equations can be used to design and optimize systems, such as bridges, buildings, and electronic circuits.
Practice Problems
To practice solving linear equations, try the following problems:
- 3x + 5 = 17
- 2x - 3 = 11
- x + 2 = 9
Conclusion
Introduction
In our previous article, we discussed how to solve linear equations using a step-by-step approach. In this article, we will answer some frequently asked questions about solving linear equations.
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable (in this case, x) is 1. It can be written in the form ax + b = c, where a, b, and c are constants.
Q: How do I solve a linear equation?
A: To solve a linear equation, you need to isolate the variable x by adding, subtracting, multiplying, or dividing both sides of the equation. You can use the following steps:
- Add or subtract the same value to both sides of the equation to eliminate the constant term.
- Multiply or divide both sides of the equation by the same value to eliminate the coefficient of x.
- Check the solution by plugging it back into the original equation.
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 (in this case, x) is 1. A quadratic equation is an equation in which the highest power of the variable (in this case, x) is 2. For example, 2x - 10 = 18 is a linear equation, while x^2 + 4x + 4 = 0 is a quadratic equation.
Q: How do I check the solution of a linear equation?
A: To check the solution of a linear equation, you need to plug the solution back into the original equation and see if it is true. For example, if the solution is x = 14, you would plug x = 14 into the original equation 2x - 10 = 18 and see if it is true.
Q: What are some common mistakes to avoid when solving linear equations?
A: Some common mistakes to avoid when solving linear equations include:
- Not isolating the variable x
- Not checking the solution
- Not following the order of operations (PEMDAS)
Q: How do I use linear equations in real-world applications?
A: Linear equations have many real-world applications, including:
- Finance: Linear equations can be used to calculate interest rates, investment returns, and other financial metrics.
- Science: Linear equations can be used to model population growth, chemical reactions, and other scientific phenomena.
- Engineering: Linear equations can be used to design and optimize systems, such as bridges, buildings, and electronic circuits.
Q: What are some examples of linear equations in real-world applications?
A: Some examples of linear equations in real-world applications include:
- Calculating the cost of a product based on its weight and price per unit
- Modeling the growth of a population based on its initial size and growth rate
- Designing a bridge based on its length, weight, and material properties
Q: How do I practice solving linear equations?
A: You can practice solving linear equations by:
- Working through practice problems, such as those found in a textbook or online resource
- Using online tools, such as a linear equation solver or a graphing calculator
- Creating your own practice problems based on real-world applications
Conclusion
Solving linear equations is a fundamental skill that has many real-world applications. By following the steps outlined in this article, you can solve linear equations and apply them to real-world problems. Remember to always check the solution by plugging it back into the original equation and to avoid common mistakes, such as not isolating the variable x and not following the order of operations (PEMDAS). With practice and patience, you can become proficient in solving linear equations and apply them to real-world problems.