Emelio Wants To Solve This Equation:$\[\frac{x}{5} = 35\\]Help Him Follow The Steps To Finish Solving For \[$x\$\].1. Multiplication Property Of Equality: \[$\frac{5}{1} \times \frac{x}{5} = 35 \times 5\$\]2. Simplify To Find
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 guide you through the steps to solve a linear equation, using Emelio's equation as an example. We will break down the solution into manageable steps, making it easy to understand and follow.
Step 1: Multiplication Property of Equality
The first step in solving a linear equation is to apply the multiplication property of equality. This property states that if we multiply both sides of an equation by the same non-zero value, the equation remains true.
Let's apply this property to Emelio's equation:
To eliminate the fraction, we can multiply both sides of the equation by 5. This is because 5 is the denominator of the fraction on the left-hand side.
By multiplying both sides by 5, we are essentially multiplying the fraction on the left-hand side by 5, which cancels out the denominator.
Step 2: Simplify to Find x
Now that we have eliminated the fraction, we can simplify the equation to find the value of x.
To find the value of x, we simply multiply 35 by 5.
Therefore, the value of x is 175.
Conclusion
Solving linear equations is a straightforward process that requires applying the multiplication property of equality and simplifying the equation to find the value of the variable. By following these steps, Emelio was able to solve his equation and find the value of x.
Real-World Applications
Linear equations have numerous real-world applications, including:
- Finance: Linear equations are used to calculate interest rates, investment returns, and loan payments.
- Science: Linear equations are used to model population growth, chemical reactions, and physical systems.
- Engineering: Linear equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.
Tips and Tricks
Here are some tips and tricks to help you solve linear equations:
- Check your work: Always check your work by plugging the solution back into the original equation.
- Use the correct operation: Make sure to use the correct operation (addition, subtraction, multiplication, or division) to solve the equation.
- Simplify the equation: Simplify the equation as much as possible to make it easier to solve.
Common Mistakes
Here are some common mistakes to avoid when solving linear equations:
- Forgetting to check your work: Always check your work to ensure that the solution is correct.
- Using the wrong operation: Make sure to use the correct operation to solve the equation.
- Not simplifying the equation: Simplify the equation as much as possible to make it easier to solve.
Conclusion
Introduction
In our previous article, we provided a step-by-step guide on how to solve linear equations. However, we understand that sometimes, you may have questions or need further clarification on certain concepts. In this article, we will address some of the most 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 (usually x) is 1. It can be written in the form ax + b = c, where a, b, and c are constants.
Q: What is the multiplication property of equality?
A: The multiplication property of equality states that if we multiply both sides of an equation by the same non-zero value, the equation remains true. This means that if we have an equation like x = 5, we can multiply both sides by 2 to get 2x = 10.
Q: How do I simplify a linear equation?
A: To simplify a linear equation, we need to combine like terms and eliminate any fractions or decimals. For example, if we have the equation 2x + 3 = 5, we can simplify it by subtracting 3 from both sides to get 2x = 2.
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 is 1, while a quadratic equation is an equation in which the highest power of the variable is 2. For example, the equation x + 2 = 3 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, we need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. For example, if we have the equation x/2 = 3/4, we can multiply both sides by 4 to get 2x = 3.
Q: What is the order of operations when solving linear equations?
A: The order of operations when solving linear equations is:
- Parentheses: Evaluate any expressions inside parentheses.
- Exponents: Evaluate any exponential expressions.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.
Q: How do I check my work when solving a linear equation?
A: To check your work when solving a linear equation, you need to plug the solution back into the original equation and verify that it is true. For example, if you solve the equation x + 2 = 3 and get x = 1, you need to plug x = 1 back into the original equation to get 1 + 2 = 3, which 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:
- Forgetting to check your work
- Using the wrong operation (e.g. adding instead of subtracting)
- Not simplifying the equation
- Not using the correct order of operations
Conclusion
Solving linear equations is a fundamental skill that is used in a wide range of applications. By understanding the concepts and techniques outlined in this article, you can solve linear equations with ease. Remember to check your work, use the correct operation, and simplify the equation to ensure that you get the correct solution.