Solve For $u$.$ 1.5(u-2) + 3.4 = 4.9 U = \square $
Introduction
In algebra, solving for a variable means isolating that variable on one side of the equation. This is a crucial skill in mathematics, as it allows us to find the value of a variable and understand the relationships between different variables. In this article, we will focus on solving for the variable u in the equation 1.5(u-2) + 3.4 = 4.9.
The Equation
The given equation is 1.5(u-2) + 3.4 = 4.9. To solve for u, we need to isolate the variable u on one side of the equation. The first step is to simplify the equation by combining like terms.
Simplifying the Equation
To simplify the equation, we can start by distributing the 1.5 to the terms inside the parentheses:
1.5(u-2) = 1.5u - 3
Now, the equation becomes:
1.5u - 3 + 3.4 = 4.9
Next, we can combine the constant terms:
-3 + 3.4 = 0.4
So, the equation becomes:
1.5u + 0.4 = 4.9
Isolating the Variable
Now that we have simplified the equation, we can isolate the variable u by subtracting 0.4 from both sides of the equation:
1.5u = 4.9 - 0.4
1.5u = 4.5
Next, we can divide both sides of the equation by 1.5 to solve for u:
u = 4.5 / 1.5
Solving for u
To solve for u, we can divide 4.5 by 1.5:
u = 3
Therefore, the value of u is 3.
Discussion
Solving for a variable is an essential skill in mathematics, as it allows us to find the value of a variable and understand the relationships between different variables. In this article, we used the equation 1.5(u-2) + 3.4 = 4.9 to demonstrate how to isolate the variable u. By simplifying the equation and isolating the variable, we were able to find the value of u, which is 3.
Conclusion
In conclusion, solving for a variable is a crucial skill in mathematics that allows us to find the value of a variable and understand the relationships between different variables. By following the steps outlined in this article, we can isolate the variable u and find its value. Whether you are a student or a professional, understanding how to solve for a variable is essential for success in mathematics.
Additional Tips and Resources
- To solve for a variable, start by simplifying the equation by combining like terms.
- Use the order of operations (PEMDAS) to simplify the equation.
- Isolate the variable by subtracting or adding the same value to both sides of the equation.
- Divide both sides of the equation by the coefficient of the variable to solve for the variable.
- Practice solving for variables by working through examples and exercises.
Common Mistakes to Avoid
- Failing to simplify the equation by combining like terms.
- Not isolating the variable by subtracting or adding the same value to both sides of the equation.
- Dividing both sides of the equation by the wrong coefficient.
- Not checking the solution by plugging it back into the original equation.
Real-World Applications
Solving for a variable has many real-world applications, including:
- Physics: Solving for variables is essential in physics to understand the relationships between different physical quantities, such as distance, velocity, and acceleration.
- Engineering: Solving for variables is crucial in engineering to design and optimize systems, such as bridges, buildings, and electronic circuits.
- Economics: Solving for variables is essential in economics to understand the relationships between different economic quantities, such as supply and demand, and to make informed decisions about investments and resource allocation.
Conclusion
Introduction
In our previous article, we demonstrated how to solve for the variable u in the equation 1.5(u-2) + 3.4 = 4.9. In this article, we will answer some frequently asked questions about solving for variables and provide additional tips and resources to help you master this essential skill.
Q&A
Q: What is the first step in solving for a variable?
A: The first step in solving for a variable is to simplify the equation by combining like terms. This involves adding or subtracting the same value to both sides of the equation to eliminate any constants.
Q: How do I know which operation to perform first?
A: To determine which operation to perform first, use the order of operations (PEMDAS):
- Parentheses: Evaluate any expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: What is the difference between isolating a variable and solving for a variable?
A: Isolating a variable means moving the variable to one side of the equation, while solving for a variable means finding the value of the variable. To solve for a variable, you must isolate the variable first.
Q: How do I know if I have isolated the variable correctly?
A: To check if you have isolated the variable correctly, plug the solution back into the original equation and verify that it is true. If the solution is not true, you may need to re-evaluate your steps.
Q: What are some common mistakes to avoid when solving for variables?
A: Some common mistakes to avoid when solving for variables include:
- Failing to simplify the equation by combining like terms.
- Not isolating the variable by subtracting or adding the same value to both sides of the equation.
- Dividing both sides of the equation by the wrong coefficient.
- Not checking the solution by plugging it back into the original equation.
Q: How can I practice solving for variables?
A: To practice solving for variables, try working through examples and exercises. You can also use online resources, such as math websites and apps, to practice solving for variables.
Q: What are some real-world applications of solving for variables?
A: Solving for variables has many real-world applications, including:
- Physics: Solving for variables is essential in physics to understand the relationships between different physical quantities, such as distance, velocity, and acceleration.
- Engineering: Solving for variables is crucial in engineering to design and optimize systems, such as bridges, buildings, and electronic circuits.
- Economics: Solving for variables is essential in economics to understand the relationships between different economic quantities, such as supply and demand, and to make informed decisions about investments and resource allocation.
Additional Tips and Resources
- To solve for a variable, start by simplifying the equation by combining like terms.
- Use the order of operations (PEMDAS) to simplify the equation.
- Isolate the variable by subtracting or adding the same value to both sides of the equation.
- Divide both sides of the equation by the coefficient of the variable to solve for the variable.
- Practice solving for variables by working through examples and exercises.
- Use online resources, such as math websites and apps, to practice solving for variables.
Real-World Examples
- A physics student is trying to calculate the distance traveled by a car. The student uses the equation d = rt to solve for the distance, where d is the distance, r is the rate, and t is the time.
- An engineer is designing a bridge and needs to calculate the stress on the bridge. The engineer uses the equation σ = F/A to solve for the stress, where σ is the stress, F is the force, and A is the area.
- An economist is trying to understand the relationship between supply and demand. The economist uses the equation Q = P × S to solve for the quantity, where Q is the quantity, P is the price, and S is the supply.
Conclusion
In conclusion, solving for variables is a crucial skill in mathematics that has many real-world applications. By following the steps outlined in this article and practicing solving for variables, you can master this essential skill and apply it to a variety of real-world problems. Whether you are a student or a professional, understanding how to solve for variables is essential for success in mathematics.