Solving Mathematical Equations Involving Subtraction and Multiplication

Understanding how to solve mathematical problems, especially those involving subtraction and multiplication, is a fundamental skill in arithmetic. This article delves into one specific type of problem often encountered in educational settings: when a certain number is subtracted from thrice a number, resulting in a particular outcome. We will not only provide the answer but also walk through the step-by-step process of solving such equations.

Example Problems

One such problem is:

[When 7 is subtracted from thrice a number the result is 14. What is the number?]

This problem requires us to set up and solve an equation. Let's denote the unknown number by x. According to the problem statement, when 7 is subtracted from thrice the number, the result is 14. Let's translate this into an equation:

3x - 7 14

To solve for x, we need to isolate x on one side of the equation. Here are the steps:

First, add 7 to both sides of the equation to eliminate the subtraction on the left side: 3x - 7 7 14 7 3x 21 Next, divide both sides of the equation by 3 to isolate x: 3x / 3 21 / 3 x 7

Therefore, the number is 7. This solution can be verified by substituting x with 7 in the original equation: 3(7) - 7 21 - 7 14. The equation holds true, confirming our answer.

Alternative Methods

Let's explore another method to approach the same problem. Suppose we have the following premises for another problem:

[7n - 5n 14]

Here, let's solve for n in a similar manner:

Combine like terms on the left side of the equation: 7n - 5n 14 2n 14 Divide both sides of the equation by 2 to isolate n: 2n / 2 14 / 2 n 7

Again, checking the solution by substituting n with 7 in the original equation: 7(7) - 5(7) 49 - 35 14, which confirms our solution.

Simplification and Verification

We can further simplify the equation 3x - 7 20 for another perspective:

First, add 7 to both sides of the equation to isolate the term with x: 3x - 7 7 20 7 3x 27 Next, divide both sides of the equation by 3 to find the value of x: 3x / 3 27 / 3 x 9

This solution can also be verified by substituting x with 9 in the original equation: 3(9) - 7 27 - 7 20. The equation indeed holds true, validating the solution.

Conclusion

Solving mathematical equations involving subtraction and multiplication is a valuable skill that can be applied in various contexts. Whether you tackle the problem as 3x - 7 14, 7n - 5n 14, or 3x - 7 20, the core process remains the same: isolate the variable by performing the same operations on both sides of the equation. With practice, these problems become quite straightforward and provide a solid foundation for more complex mathematical concepts.