Solve For R R R .${ \frac{r+2}{8} = \frac{3}{2} }$r =$

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Introduction

In algebra, solving for a variable involves isolating it on one side of the equation. This is a crucial skill that is used extensively in various mathematical operations. In this article, we will focus on solving for the variable rr in the given equation r+28=32\frac{r+2}{8} = \frac{3}{2}. We will break down the solution into manageable steps and provide a clear explanation of each step.

Step 1: Multiply Both Sides by the Denominator

The first step in solving for rr is to eliminate the fraction by multiplying both sides of the equation by the denominator. In this case, the denominator is 8.

r+28=32\frac{r+2}{8} = \frac{3}{2}

Multiply both sides by 8:

(r+2)=8×32(r+2) = 8 \times \frac{3}{2}

Step 2: Simplify the Right-Hand Side

Now, let's simplify the right-hand side of the equation by multiplying 8 and 32\frac{3}{2}.

(r+2)=8×32(r+2) = 8 \times \frac{3}{2}

=8×1.5= 8 \times 1.5

=12= 12

Step 3: Isolate the Variable rr

Now that we have simplified the right-hand side, we can isolate the variable rr by subtracting 2 from both sides of the equation.

(r+2)=12(r+2) = 12

Subtract 2 from both sides:

r+2−2=12−2r+2-2 = 12-2

r=10r = 10

Conclusion

In this article, we have solved for the variable rr in the given equation r+28=32\frac{r+2}{8} = \frac{3}{2}. We have broken down the solution into manageable steps and provided a clear explanation of each step. By following these steps, you should be able to solve for rr in any similar equation.

Frequently Asked Questions

Q: What is the value of rr in the given equation?

A: The value of rr is 10.

Q: How do I solve for rr in a similar equation?

A: To solve for rr, multiply both sides of the equation by the denominator, simplify the right-hand side, and isolate the variable rr by subtracting the constant term from both sides.

Q: What is the importance of solving for a variable?

A: Solving for a variable is a crucial skill in algebra that is used extensively in various mathematical operations. It allows us to isolate the variable and understand its relationship with other variables in the equation.

Tips and Tricks

  • When solving for a variable, make sure to follow the order of operations (PEMDAS) to simplify the equation.
  • Use algebraic properties such as the distributive property and the commutative property to simplify the equation.
  • Check your solution by plugging it back into the original equation to ensure that it is true.

Real-World Applications

Solving for a variable has numerous real-world applications in fields such as physics, engineering, and economics. For example, in physics, solving for a variable can help us understand the relationship between different physical quantities such as distance, time, and velocity. In engineering, solving for a variable can help us design and optimize systems such as bridges, buildings, and electronic circuits. In economics, solving for a variable can help us understand the relationship between different economic variables such as supply and demand, inflation, and unemployment.

Final Thoughts

Solving for a variable is a fundamental skill in algebra that is used extensively in various mathematical operations. By following the steps outlined in this article, you should be able to solve for rr in any similar equation. Remember to always follow the order of operations, use algebraic properties to simplify the equation, and check your solution by plugging it back into the original equation. With practice and patience, you will become proficient in solving for variables and be able to apply this skill to real-world problems.

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Q: What is the value of rr in the given equation r+28=32\frac{r+2}{8} = \frac{3}{2}?

A: The value of rr is 10.

Q: How do I solve for rr in a similar equation?

A: To solve for rr, multiply both sides of the equation by the denominator, simplify the right-hand side, and isolate the variable rr by subtracting the constant term from both sides.

Q: What is the importance of solving for a variable?

A: Solving for a variable is a crucial skill in algebra that is used extensively in various mathematical operations. It allows us to isolate the variable and understand its relationship with other variables in the equation.

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 following the order of operations (PEMDAS)
  • Not simplifying the equation properly
  • Not checking the solution by plugging it back into the original equation
  • Not using algebraic properties such as the distributive property and the commutative property to simplify the equation

Q: How do I check my solution to ensure that it is true?

A: To check your solution, plug it back into the original equation and simplify. If the equation is true, then your solution is correct.

Q: What are some real-world applications of solving for a variable?

A: Solving for a variable has numerous real-world applications in fields such as physics, engineering, and economics. For example, in physics, solving for a variable can help us understand the relationship between different physical quantities such as distance, time, and velocity. In engineering, solving for a variable can help us design and optimize systems such as bridges, buildings, and electronic circuits. In economics, solving for a variable can help us understand the relationship between different economic variables such as supply and demand, inflation, and unemployment.

Q: Can I use a calculator to solve for a variable?

A: Yes, you can use a calculator to solve for a variable. However, it is always a good idea to check your solution by plugging it back into the original equation to ensure that it is true.

Q: What are some tips for solving for a variable?

A: Some tips for solving for a variable include:

  • Follow the order of operations (PEMDAS)
  • Simplify the equation properly
  • Use algebraic properties such as the distributive property and the commutative property to simplify the equation
  • Check your solution by plugging it back into the original equation

Q: Can I solve for a variable with a negative exponent?

A: Yes, you can solve for a variable with a negative exponent. To do this, use the property of negative exponents, which states that a−n=1ana^{-n} = \frac{1}{a^n}.

Q: What are some common equations that involve solving for a variable?

A: Some common equations that involve solving for a variable include:

  • Linear equations: ax+b=cax + b = c
  • Quadratic equations: ax2+bx+c=0ax^2 + bx + c = 0
  • Polynomial equations: anxn+an−1xn−1+…+a1x+a0=0a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0 = 0

Q: Can I solve for a variable with a fraction as a coefficient?

A: Yes, you can solve for a variable with a fraction as a coefficient. To do this, multiply both sides of the equation by the denominator of the fraction.

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

A: Some advanced techniques for solving for a variable include:

  • Using algebraic properties such as the distributive property and the commutative property to simplify the equation
  • Using substitution and elimination methods to solve for a variable
  • Using graphing and other visual methods to solve for a variable

Q: Can I solve for a variable with a system of equations?

A: Yes, you can solve for a variable with a system of equations. To do this, use the substitution and elimination methods to solve for the variables in the system.

Q: What are some common mistakes to avoid when solving for a variable in a system of equations?

A: Some common mistakes to avoid when solving for a variable in a system of equations include:

  • Not following the order of operations (PEMDAS)
  • Not simplifying the equation properly
  • Not checking the solution by plugging it back into the original equation
  • Not using algebraic properties such as the distributive property and the commutative property to simplify the equation