Solving for a Number: Three Times a Number Increased by 3 Equals 30

Understanding and solving algebraic equations is a fundamental skill in mathematics. A common type of equation that students encounter is one where a number is defined through a series of operations. In this article, we will explore how to solve an equation where 'three times a number increased by 3 equals 30'. This problem not only reinforces basic algebraic concepts but also provides a clear step-by-step approach to solving such equations.

Introduction to the Problem

The problem statement is: 'Three times a number increased by 3 is equal to 30'. Mathematically, this can be expressed as:

3x 3 30

Solving the Equation

To solve for x, we will follow a systematic approach to isolate the variable:

Step 1: Isolate the Term with the Variable

First, we need to isolate the term that contains the variable x. We do this by subtracting 3 from both sides of the equation:

3x 3 - 3 30 - 3

This simplifies to:

3x 27

Step 2: Solve for x

Next, we divide both sides of the equation by 3 to isolate x:

3x / 3 27 / 3

Which simplifies to:

x 9

So, the solution to the equation is x 9.

Verification

To verify the solution, we can substitute x 9 back into the original equation:

3(9) 3 30

This simplifies to:

27 3 30

30 30

This confirms that our solution is correct.

Alternative Methods

While the systematic approach provides a clear and structured way to solve the equation, there are other methods that can be employed, such as guess and check, which might be less efficient but can still lead to the correct answer.

Guess and Check Method

Using the guess and check method, we can start by testing different values for x until we find the correct value:

1. If x 8: 3(8) 3 27, which is not 30.

2. If x 9: 3(9) 3 27 3 30, which is correct.

This method, although not as efficient, can be useful for simpler equations.

Conclusion

In conclusion, solving the equation 'three times a number increased by 3 equals 30' involves a clear and methodical approach. By following the steps of isolating the variable and then solving for it, we can find the solution and verify it. This type of algebraic problem is a stepping stone to more complex mathematical concepts and provides a solid foundation for further studies in mathematics.