Solve The Equation:${ 0.08(7.97 + V) = 0.832 }$

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Introduction

In this article, we will focus on solving a linear equation involving a variable. The equation is given as 0.08(7.97 + v) = 0.832, where v is the variable we need to solve for. We will use algebraic techniques to isolate the variable and find its value.

Understanding the Equation

The given equation is a linear equation, which means it can be written in the form of ax + b = c, where a, b, and c are constants. In this case, the equation can be rewritten as 0.08(7.97 + v) = 0.832. To solve for v, we need to isolate the variable on one side of the equation.

Distributive Property

To start solving the equation, we can use the distributive property to expand the left-hand side of the equation. The distributive property states that a(b + c) = ab + ac. In this case, we can apply the distributive property to expand 0.08(7.97 + v) as follows:

0.08(7.97 + v) = 0.08(7.97) + 0.08(v)

Simplifying the Equation

Now that we have expanded the left-hand side of the equation, we can simplify it by evaluating the expression 0.08(7.97). This gives us:

0.08(7.97) = 0.6396

So, the equation becomes:

0.6396 + 0.08(v) = 0.832

Isolating the Variable

To isolate the variable v, we need to get rid of the constant term 0.6396 on the left-hand side of the equation. We can do this by subtracting 0.6396 from both sides of the equation:

0.08(v) = 0.832 - 0.6396

Evaluating the Right-Hand Side

Now, we need to evaluate the right-hand side of the equation by subtracting 0.6396 from 0.832:

0.832 - 0.6396 = 0.1924

So, the equation becomes:

0.08(v) = 0.1924

Solving for v

To solve for v, we need to get rid of the coefficient 0.08 on the left-hand side of the equation. We can do this by dividing both sides of the equation by 0.08:

v = 0.1924 / 0.08

Evaluating the Right-Hand Side

Now, we need to evaluate the right-hand side of the equation by dividing 0.1924 by 0.08:

0.1924 / 0.08 = 2.403

So, the value of v is 2.403.

Conclusion

In this article, we solved a linear equation involving a variable. We used algebraic techniques to isolate the variable and find its value. The equation was given as 0.08(7.97 + v) = 0.832, and we solved for v by using the distributive property, simplifying the equation, isolating the variable, and solving for v. The value of v is 2.403.

Frequently Asked Questions

  • What is the distributive property? The distributive property is a mathematical property that states that a(b + c) = ab + ac.
  • How do I simplify an equation? To simplify an equation, you can use algebraic techniques such as combining like terms, evaluating expressions, and isolating variables.
  • How do I solve for a variable? To solve for a variable, you can use algebraic techniques such as isolating the variable, using inverse operations, and evaluating expressions.

Related Topics

  • Linear Equations
  • Algebraic Techniques
  • Distributive Property
  • Simplifying Equations
  • Solving for Variables

References

  • [1] "Algebra" by Michael Artin
  • [2] "Linear Algebra" by Jim Hefferon
  • [3] "Mathematics for Computer Science" by Eric Lehman

Keywords

  • Linear Equation
  • Algebraic Techniques
  • Distributive Property
  • Simplifying Equations
  • Solving for Variables
  • Mathematics
  • Algebra
  • Linear Algebra

Introduction

In our previous article, we solved a linear equation involving a variable. In this article, we will answer some frequently asked questions related to solving linear equations. We will cover topics such as the distributive property, simplifying equations, and solving for variables.

Q&A

Q: What is the distributive property?

A: The distributive property is a mathematical property that states that a(b + c) = ab + ac. This property allows us to expand expressions and simplify equations.

Q: How do I simplify an equation?

A: To simplify an equation, you can use algebraic techniques such as combining like terms, evaluating expressions, and isolating variables. For example, if you have the equation 2x + 3x = 5, you can combine like terms by adding 2x and 3x to get 5x = 5.

Q: How do I solve for a variable?

A: To solve for a variable, you can use algebraic techniques such as isolating the variable, using inverse operations, and evaluating expressions. For example, if you have the equation 2x = 5, you can solve for x by dividing both sides of the equation by 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. For example, the equation 2x + 3 = 5 is a linear equation. A quadratic equation, on the other hand, is an equation in which the highest power of the variable is 2. For example, the equation x^2 + 2x + 1 = 0 is a quadratic equation.

Q: How do I know if an equation is linear or quadratic?

A: To determine if an equation is linear or quadratic, you can look at the highest power of the variable. If the highest power is 1, the equation is linear. If the highest power is 2, the equation is quadratic.

Q: Can I use the distributive property to solve a quadratic equation?

A: No, the distributive property is used to expand expressions and simplify equations, but it is not used to solve quadratic equations. To solve a quadratic equation, you can use techniques such as factoring, completing the square, or using the quadratic formula.

Q: What is the quadratic formula?

A: The quadratic formula is a formula that is used to solve quadratic equations. The formula is x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the quadratic equation.

Q: How do I use the quadratic formula to solve a quadratic equation?

A: To use the quadratic formula, you need to identify the coefficients a, b, and c in the quadratic equation. Then, you can plug these values into the formula and simplify to find the solutions.

Q: Can I use a calculator to solve a quadratic equation?

A: Yes, you can use a calculator to solve a quadratic equation. Many calculators have a built-in quadratic formula function that you can use to find the solutions.

Conclusion

In this article, we answered some frequently asked questions related to solving linear equations. We covered topics such as the distributive property, simplifying equations, and solving for variables. We also discussed the difference between linear and quadratic equations and how to use the quadratic formula to solve quadratic equations.

Frequently Asked Questions

  • What is the distributive property?
  • How do I simplify an equation?
  • How do I solve for a variable?
  • What is the difference between a linear equation and a quadratic equation?
  • How do I know if an equation is linear or quadratic?
  • Can I use the distributive property to solve a quadratic equation?
  • What is the quadratic formula?
  • How do I use the quadratic formula to solve a quadratic equation?
  • Can I use a calculator to solve a quadratic equation?

Related Topics

  • Linear Equations
  • Algebraic Techniques
  • Distributive Property
  • Simplifying Equations
  • Solving for Variables
  • Quadratic Equations
  • Quadratic Formula

References

  • [1] "Algebra" by Michael Artin
  • [2] "Linear Algebra" by Jim Hefferon
  • [3] "Mathematics for Computer Science" by Eric Lehman

Keywords

  • Linear Equation
  • Algebraic Techniques
  • Distributive Property
  • Simplifying Equations
  • Solving for Variables
  • Quadratic Equation
  • Quadratic Formula
  • Mathematics
  • Algebra
  • Linear Algebra