Solve For \[$ R \$\].$\[ \begin{aligned} \frac{r}{5} - 6 &= 2 \\ r &= \,? \end{aligned} \\]

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Solving for r: A Step-by-Step Guide to Isolating the Variable

In mathematics, solving for a variable is a fundamental concept that involves isolating the variable on one side of the equation. In this article, we will focus on solving for the variable r in the given equation. We will break down the solution into manageable steps, making it easy to understand and follow along.

Understanding the Equation

The given equation is:

r5−6=2\frac{r}{5} - 6 = 2

Our goal is to isolate the variable r on one side of the equation. To do this, we need to get rid of the fraction and the constant term on the same side as r.

Step 1: Add 6 to Both Sides

The first step is to add 6 to both sides of the equation to get rid of the constant term on the same side as r.

r5−6+6=2+6\frac{r}{5} - 6 + 6 = 2 + 6

This simplifies to:

r5=8\frac{r}{5} = 8

Step 2: Multiply Both Sides by 5

Next, we need to get rid of the fraction by multiplying both sides of the equation by 5.

r5×5=8×5\frac{r}{5} \times 5 = 8 \times 5

This simplifies to:

r=40r = 40

In this article, we solved for the variable r in the given equation. We broke down the solution into manageable steps, making it easy to understand and follow along. By adding 6 to both sides of the equation and then multiplying both sides by 5, we were able to isolate the variable r on one side of the equation.

  • When solving for a variable, it's essential to get rid of any fractions by multiplying both sides of the equation by the denominator.
  • Adding or subtracting the same value to both sides of the equation is a common technique used to isolate the variable.
  • Make sure to simplify the equation at each step to avoid any confusion.

Solving for a variable is a fundamental concept that has numerous real-world applications. In physics, for example, solving for a variable can help us understand the motion of objects and the forces acting upon them. In engineering, solving for a variable can help us design and optimize systems.

  • Not simplifying the equation at each step can lead to confusion and incorrect solutions.
  • Failing to get rid of fractions can make it difficult to isolate the variable.
  • Not checking the solution by plugging it back into the original equation can lead to incorrect solutions.

Solving for a variable is a fundamental concept in mathematics that has numerous real-world applications. By following the steps outlined in this article, you can easily isolate the variable r in the given equation. Remember to simplify the equation at each step, get rid of fractions, and check the solution by plugging it back into the original equation.
Solving for r: A Q&A Guide to Mastering the Concept

In our previous article, we explored the concept of solving for a variable, specifically the variable r in the equation r5−6=2\frac{r}{5} - 6 = 2. We broke down the solution into manageable steps and provided tips and tricks for mastering the concept. In this article, we will answer some of the most frequently asked questions about solving for a variable.

Q: What is the first step in solving for a variable?

A: The first step in solving for a variable is to get rid of any fractions by multiplying both sides of the equation by the denominator.

Q: How do I get rid of a fraction in an equation?

A: To get rid of a fraction in an equation, multiply both sides of the equation by the denominator. For example, if the equation is x2=3\frac{x}{2} = 3, multiply both sides by 2 to get rid of the fraction.

Q: What is the difference between adding and subtracting the same value to both sides of an equation?

A: Adding and subtracting the same value to both sides of an equation are two different techniques used to isolate the variable. Adding the same value to both sides of an equation is used to get rid of a constant term, while subtracting the same value from both sides of an equation is used to get rid of a variable term.

Q: How do I check my solution to an equation?

A: To check your solution to an equation, plug the solution back into the original equation and verify that it is true. For example, if the equation is x+2=5x + 2 = 5 and the solution is x=3x = 3, plug x=3x = 3 back into the equation to verify that it is true.

Q: What are some common mistakes to avoid when solving for a variable?

A: Some common mistakes to avoid when solving for a variable include not simplifying the equation at each step, failing to get rid of fractions, and not checking the solution by plugging it back into the original equation.

Q: How do I apply the concept of solving for a variable to real-world problems?

A: The concept of solving for a variable can be applied to a wide range of real-world problems, including physics, engineering, and economics. For example, in physics, solving for a variable can help us understand the motion of objects and the forces acting upon them. In engineering, solving for a variable can help us design and optimize systems.

Q: What are some advanced techniques for solving for a variable?

A: Some advanced techniques for solving for a variable include using algebraic manipulations, such as factoring and expanding expressions, and using numerical methods, such as the quadratic formula.

Solving for a variable is a fundamental concept in mathematics that has numerous real-world applications. By following the steps outlined in this article and avoiding common mistakes, you can master the concept of solving for a variable and apply it to a wide range of problems.

  • Khan Academy: Solving Equations
  • Mathway: Solving Equations
  • Wolfram Alpha: Solving Equations
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