Solve For $v$:$-4v = \frac{12}{5}$Simplify Your Answer As Much As Possible.$v =$
Introduction
In this article, we will focus on solving for the variable v in a linear equation. The equation given is -4v = 12/5. We will use algebraic methods to isolate the variable v and simplify the expression.
Understanding the Equation
The given equation is -4v = 12/5. This is a linear equation, where the variable v is multiplied by a constant -4. To solve for v, we need to isolate the variable on one side of the equation.
Step 1: Multiply Both Sides by the Reciprocal of -4
To isolate the variable v, we need to get rid of the coefficient -4. We can do this by multiplying both sides of the equation by the reciprocal of -4, which is -1/4.
-4v = 12/5
(-1/4) * (-4v) = (-1/4) * (12/5)
v = -3/5
Simplifying the Expression
The expression -3/5 is already simplified. However, we can further simplify it by expressing it as a decimal or a fraction with a smaller denominator.
v = -3/5 = -0.6
Conclusion
In this article, we solved for the variable v in the linear equation -4v = 12/5. We used algebraic methods to isolate the variable v and simplify the expression. The final answer is v = -3/5.
Tips and Tricks
- When solving for a variable in a linear equation, make sure to isolate the variable on one side of the equation.
- Use the reciprocal of the coefficient to get rid of it.
- Simplify the expression by expressing it as a decimal or a fraction with a smaller denominator.
Real-World Applications
Solving for variables in linear equations has many real-world applications. For example, in physics, we use linear equations to describe the motion of objects. In finance, we use linear equations to calculate interest rates and investment returns.
Common Mistakes
- Not isolating the variable on one side of the equation.
- Not using the reciprocal of the coefficient to get rid of it.
- Not simplifying the expression.
Practice Problems
- Solve for x in the equation 2x = 12.
- Solve for y in the equation -3y = 9.
- Solve for z in the equation 4z = 24.
Answer Key
- x = 6
- y = -3
- z = 6
Solving for v in a Linear Equation: Q&A =====================================
Introduction
In our previous article, we solved for the variable v in the linear equation -4v = 12/5. We used algebraic methods to isolate the variable v and simplify the expression. In this article, we will answer some frequently asked questions about solving for variables in linear equations.
Q: What is a linear equation?
A: A linear equation is an equation in which the highest power of the variable is 1. In other words, it is an equation in which the variable is not raised to a power greater than 1.
Q: How do I solve for a variable in a linear equation?
A: To solve for a variable in a linear equation, you need to isolate the variable on one side of the equation. You can do this by using algebraic methods such as addition, subtraction, multiplication, and division.
Q: What is the reciprocal of a number?
A: The reciprocal of a number is 1 divided by that number. For example, the reciprocal of 4 is 1/4.
Q: How do I use the reciprocal to solve for a variable?
A: To use the reciprocal to solve for a variable, you need to multiply both sides of the equation by the reciprocal of the coefficient of the variable. This will get rid of the coefficient and isolate the variable.
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.
Q: How do I solve for a variable in a quadratic equation?
A: To solve for a variable in a quadratic equation, you need to use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. This formula will give you two solutions for the variable.
Q: What is the quadratic formula?
A: The quadratic formula is a formula used to solve quadratic equations. It is: x = (-b ± √(b^2 - 4ac)) / 2a.
Q: How do I use the quadratic formula to solve for a variable?
A: To use the quadratic formula to solve for a variable, you need to plug in the values of a, b, and c into the formula. This will give you two solutions for the variable.
Q: What are some common mistakes to avoid when solving for variables in linear equations?
A: Some common mistakes to avoid when solving for variables in linear equations include:
- Not isolating the variable on one side of the equation
- Not using the reciprocal of the coefficient to get rid of it
- Not simplifying the expression
Q: How do I simplify an expression?
A: To simplify an expression, you need to combine like terms and eliminate any unnecessary parentheses.
Q: What are some real-world applications of solving for variables in linear equations?
A: Some real-world applications of solving for variables in linear equations include:
- Physics: solving for the motion of objects
- Finance: calculating interest rates and investment returns
- Engineering: designing buildings and bridges
Conclusion
In this article, we answered some frequently asked questions about solving for variables in linear equations. We covered topics such as what a linear equation is, how to solve for a variable, and some common mistakes to avoid. We also discussed some real-world applications of solving for variables in linear equations.
Practice Problems
- Solve for x in the equation 2x = 12.
- Solve for y in the equation -3y = 9.
- Solve for z in the equation 4z = 24.
Answer Key
- x = 6
- y = -3
- z = 6