Solving Algebraic Expressions: Finding the Value of 4x - 3

Understanding and solving algebraic expressions is a fundamental skill in mathematics, especially when dealing with equations and expressions involving variables. In this article, we will explore the process in a detailed step-by-step guide. We will follow an example where the initial equation is given, and we need to find the value of 4x - 3 based on given conditions. Our objective is to break down the problem into simple algebraic steps and understand the underlying logic behind each step.

Understanding the Given Equation: 4x - 3

Consider the statement: If 4x - 3 12, what is the value of 4x - 3? It seems counterintuitive at first glance, but the key is to understand that we need to solve for x first and then substitute it back into the expression to find the value of 4x - 3.

Solving the Initial Equation: 4x - 3 12

To solve for x, we first isolate 4x by adding 3 to both sides of the equation:

[4x - 3 3 12 3]

This simplifies to:

[4x 15]

Next, we solve for x by dividing both sides of the equation by 4:

[x frac{15}{4}]

Substituting the Value of x into 4x - 3

Now that we have the value of x, we can substitute it back into the expression 4x - 3 to find its value:

[4x - 3 4left(frac{15}{4}right) - 3]

Simplifying the expression:

[4x - 3 15 - 3 12]

Therefore, the value of 4x - 3 when 4x - 3 12 is 12.

Alternative Method: Verifying the Given Equation

Another way to approach the problem is to understand the relationship between the expressions 4x - 3 and 4x 3. Notice that:

[4x - 3 4x 3 - 6]

This shows that the expression 4x - 3 is 6 less than the expression 4x 3. If we solve the initial equation: 4x 3 12, we can directly use this relationship to find the value of 4x - 3.

Step-by-Step Solution for 4x 3 12

First, isolate 4x by subtracting 3 from both sides:

[4x 3 - 3 12 - 3]

This simplifies to:

[4x 9]

Now, solve for x by dividing both sides by 4:

[x frac{9}{4}]

Next, use the relationship between 4x 3 and 4x - 3. Since 4x - 3 is 6 less than 4x 3, we have:

[4x - 3 12 - 6 6]

Hence, the value of 4x - 3 is 6.

Conclusion

In this article, we explored the process of solving algebraic expressions and found the value of 4x - 3 given the initial equation. By following step-by-step algebraic methods, we derived that the value of 4x - 3 is 6. This problem demonstrates the importance of logical and systematic approaches in solving algebraic expressions, which are essential skills in mathematical problem-solving.