Solve The Two-step Equation.Examine The Worked Problem And Solve The Equation.${ \begin{aligned} \frac{4}{3}(x)-\frac{1}{3} & =9 \ \frac{4}{3}(x)-\frac{1}{3}+\frac{1}{3} & =9+\frac{1}{3} \ \frac{4}{3}(x) & =\frac{28}{3} \end{aligned} }$The
Introduction
Solving two-step equations is a fundamental concept in algebra that requires a clear understanding of the steps involved. In this article, we will examine a worked problem and provide a step-by-step guide on how to solve the equation. We will also discuss the importance of two-step equations in mathematics and provide examples of real-world applications.
What are Two-Step Equations?
Two-step equations are algebraic equations that require two steps to solve. These equations involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving a two-step equation is to isolate the variable and find its value.
The Worked Problem
Let's examine the following two-step equation:
{ \begin{aligned} \frac{4}{3}(x)-\frac{1}{3} & =9 \\ \frac{4}{3}(x)-\frac{1}{3}+\frac{1}{3} & =9+\frac{1}{3} \\ \frac{4}{3}(x) & =\frac{28}{3} \end{aligned} \}
Step 1: Simplify the Equation
The first step in solving the equation is to simplify it by combining like terms. In this case, we can add to both sides of the equation to eliminate the negative term.
{ \begin{aligned} \frac{4}{3}(x)-\frac{1}{3}+\frac{1}{3} & =9+\frac{1}{3} \\ \frac{4}{3}(x) & =\frac{28}{3} \end{aligned} \}
Step 2: Isolate the Variable
The next step is to isolate the variable by dividing both sides of the equation by .
{ \begin{aligned} \frac{4}{3}(x) & =\frac{28}{3} \\ x & =\frac{28}{3} \div \frac{4}{3} \\ x & =7 \end{aligned} \}
Conclusion
Solving two-step equations requires a clear understanding of the steps involved. By simplifying the equation and isolating the variable, we can find the value of the variable. In this article, we examined a worked problem and provided a step-by-step guide on how to solve the equation. We also discussed the importance of two-step equations in mathematics and provided examples of real-world applications.
Real-World Applications
Two-step equations have numerous real-world applications in fields such as physics, engineering, and economics. For example, in physics, two-step equations can be used to calculate the velocity and acceleration of an object. In engineering, two-step equations can be used to design and optimize systems such as bridges and buildings. In economics, two-step equations can be used to model and analyze economic systems.
Tips and Tricks
Here are some tips and tricks to help you solve two-step equations:
- Simplify the equation: Before solving the equation, simplify it by combining like terms.
- Isolate the variable: Once you have simplified the equation, isolate the variable by dividing both sides of the equation by the coefficient of the variable.
- Check your answer: Once you have found the value of the variable, check your answer by plugging it back into the original equation.
Common Mistakes
Here are some common mistakes to avoid when solving two-step equations:
- Not simplifying the equation: Failing to simplify the equation can lead to incorrect solutions.
- Not isolating the variable: Failing to isolate the variable can lead to incorrect solutions.
- Not checking your answer: Failing to check your answer can lead to incorrect solutions.
Conclusion
Introduction
In our previous article, we examined a worked problem and provided a step-by-step guide on how to solve a two-step equation. In this article, we will answer some frequently asked questions about two-step equations.
Q: What is a two-step equation?
A: A two-step equation is an algebraic equation that requires two steps to solve. These equations involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
Q: How do I simplify a two-step equation?
A: To simplify a two-step equation, combine like terms by adding or subtracting the coefficients of the same variable.
Q: How do I isolate the variable in a two-step equation?
A: To isolate the variable in a two-step equation, divide both sides of the equation by the coefficient of the variable.
Q: What is the difference between a two-step equation and a one-step equation?
A: A one-step equation is an algebraic equation that requires only one step to solve. A two-step equation, on the other hand, requires two steps to solve.
Q: Can I use a calculator to solve a two-step equation?
A: Yes, you can use a calculator to solve a two-step equation. However, it's always a good idea to check your answer by plugging it back into the original equation.
Q: What are some common mistakes to avoid when solving two-step equations?
A: Some common mistakes to avoid when solving two-step equations include:
- Not simplifying the equation
- Not isolating the variable
- Not checking your answer
Q: How do I check my answer when solving a two-step equation?
A: To check your answer when solving a two-step equation, plug the value of the variable back into the original equation and simplify. If the equation is true, then your answer is correct.
Q: Can I use two-step equations to solve real-world problems?
A: Yes, two-step equations can be used to solve real-world problems in fields such as physics, engineering, and economics.
Q: What are some examples of real-world applications of two-step equations?
A: Some examples of real-world applications of two-step equations include:
- Calculating the velocity and acceleration of an object in physics
- Designing and optimizing systems such as bridges and buildings in engineering
- Modeling and analyzing economic systems in economics
Conclusion
Solving two-step equations is a fundamental concept in algebra that requires a clear understanding of the steps involved. By simplifying the equation and isolating the variable, we can find the value of the variable. In this article, we answered some frequently asked questions about two-step equations and provided examples of real-world applications.
Additional Resources
For more information on two-step equations, check out the following resources:
- Khan Academy: Two-Step Equations
- Mathway: Two-Step Equations
- Algebra.com: Two-Step Equations
Practice Problems
Try solving the following two-step equations: