M6|L10 Different Options For Solving One EquationSign Out Divide Each Side By The Same Value So That One Group Of X 4 3 ​ Remains On The Left. Then, Rewrite The Equation. 3 4 ​ (x 4 3 ​ ) = 5

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Introduction

Solving equations is a fundamental concept in mathematics, and it's essential to understand the different methods and techniques used to solve them. In this article, we will explore different options for solving one equation, specifically the equation (x 4 3 ​ ) = 5. We will discuss the steps involved in solving this equation and provide examples to illustrate the different methods.

Option 1: Divide Each Side by the Same Value

One of the most common methods for solving equations is to divide each side by the same value. This method is used to isolate the variable, in this case, x. To solve the equation (x 4 3 ​ ) = 5, we need to divide each side by ( 4 3 ​ ).

Step 1: Divide Each Side by ( 4 3 ​ )

To divide each side by ( 4 3 ​ ), we need to multiply the reciprocal of ( 4 3 ​ ), which is ( 3 4 ​ ), by each side of the equation.

(x 4 3 ​ ) = 5

Multiply each side by ( 3 4 ​ ):

( 3 4 ​ ) (x 4 3 ​ ) = ( 3 4 ​ ) (5)

Simplify the equation:

x = ( 3 4 ​ ) (5)

Step 2: Simplify the Equation

To simplify the equation, we need to multiply ( 3 4 ​ ) by 5.

x = ( 3 4 ​ ) (5)

x = 15/4

Step 3: Check the Solution

To check the solution, we need to substitute x = 15/4 back into the original equation.

(x 4 3 ​ ) = 5

Substitute x = 15/4:

( 15/4 4 3 ​ ) = 5

Simplify the equation:

( 15/4 4 3 ​ ) = 5

x = 15/4

The solution x = 15/4 satisfies the original equation.

Option 2: Multiply Each Side by the Same Value

Another method for solving equations is to multiply each side by the same value. This method is used to eliminate the fraction and make the equation easier to solve.

Step 1: Multiply Each Side by ( 4 3 ​ )

To multiply each side by ( 4 3 ​ ), we need to multiply ( 4 3 ​ ) by each side of the equation.

(x 4 3 ​ ) = 5

Multiply each side by ( 4 3 ​ ):

( 4 3 ​ ) (x 4 3 ​ ) = ( 4 3 ​ ) (5)

Simplify the equation:

x = ( 4 3 ​ ) (5)

Step 2: Simplify the Equation

To simplify the equation, we need to multiply ( 4 3 ​ ) by 5.

x = ( 4 3 ​ ) (5)

x = 20/3

Step 3: Check the Solution

To check the solution, we need to substitute x = 20/3 back into the original equation.

(x 4 3 ​ ) = 5

Substitute x = 20/3:

( 20/3 4 3 ​ ) = 5

Simplify the equation:

( 20/3 4 3 ​ ) = 5

x = 20/3

The solution x = 20/3 satisfies the original equation.

Conclusion

In this article, we explored different options for solving one equation, specifically the equation (x 4 3 ​ ) = 5. We discussed the steps involved in solving this equation using two different methods: dividing each side by the same value and multiplying each side by the same value. We provided examples to illustrate the different methods and checked the solutions to ensure that they satisfy the original equation. These methods can be applied to solve a wide range of equations, and it's essential to understand the different techniques used to solve them.

References

Additional Resources

Introduction

In our previous article, we explored different options for solving one equation, specifically the equation (x 4 3 ​ ) = 5. We discussed the steps involved in solving this equation using two different methods: dividing each side by the same value and multiplying each side by the same value. In this article, we will answer some frequently asked questions related to solving equations.

Q&A

Q: What is the first step in solving an equation?

A: The first step in solving an equation is to isolate the variable, in this case, x. This can be done by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: How do I know which method to use to solve an equation?

A: The method you use to solve an equation depends on the type of equation and the values involved. If the equation has a fraction, you may need to multiply or divide both sides by the same value to eliminate the fraction. If the equation has a variable with a coefficient, you may need to use the distributive property to simplify the equation.

Q: What is the distributive property?

A: The distributive property is a mathematical property that allows you to multiply a single value by multiple values. For example, a(b + c) = ab + ac.

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

A: To check your solution to an equation, you need to substitute the value of the variable back into the original equation and simplify. If the equation is true, then your solution is correct.

Q: What are some common mistakes to avoid when solving equations?

A: Some common mistakes to avoid when solving equations include:

  • Not isolating the variable
  • Not simplifying the equation
  • Not checking the solution
  • Not using the correct method to solve the equation

Q: How do I solve an equation with a variable on both sides?

A: To solve an equation with a variable on both sides, you need to add or subtract the same value from both sides of the equation to eliminate the variable on one side. Then, you can isolate the variable on the other side.

Q: How do I solve an equation with a fraction?

A: To solve an equation with a fraction, you need to multiply or divide both sides of the equation by the same value to eliminate the fraction.

Q: What is the order of operations when solving equations?

A: The order of operations when solving equations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Conclusion

In this article, we answered some frequently asked questions related to solving equations. We discussed the steps involved in solving equations, including isolating the variable, simplifying the equation, and checking the solution. We also covered some common mistakes to avoid when solving equations and the order of operations when solving equations. By following these steps and avoiding common mistakes, you can become proficient in solving equations and tackle even the most challenging problems.

References

Additional Resources