Understanding the Equation 2x - 3 = 7
The equation 2x - 3 = 7 is a linear equation where the goal is to find the value of x that makes the equation true. To solve it, isolate x by performing inverse operations on both sides, maintaining equality. Start by adding 3 to both sides to undo the subtraction: 2x - 3 + 3 = 7 + 3, which simplifies to 2x = 10.
Key Principles of Solving Linear Equations
The core principles involve the properties of equality: whatever operation is applied to one side must be applied to the other. Here, addition reverses subtraction, and division reverses multiplication. After getting 2x = 10, divide both sides by 2: 2x / 2 = 10 / 2, resulting in x = 5. Always verify by substituting x back into the original equation: 2(5) - 3 = 10 - 3 = 7, which holds true.
Practical Example: Applying the Steps
Consider a real-world scenario, like budgeting: if 2x - 3 represents twice the number of items minus a fixed cost equaling $7, solving for x finds the number of items. Following the steps: add 3 to get 2x = 10, then divide by 2 to get x = 5. This means 5 items fit the budget, illustrating how algebra solves everyday problems.
Importance of Step-by-Step Solving
Mastering this process builds foundational algebra skills essential for higher math, science, and engineering. It teaches logical problem-solving and error prevention, such as avoiding common mistakes like forgetting to apply operations to both sides. Understanding these steps empowers tackling more complex equations in academics and professional applications.