Solve......................................................................

To solve a mathematical problem effectively, it's essential to break it down into manageable steps. Let's consider a specific example to illustrate this process. Suppose we need to solve the equation 2x + 3 = 11. Here’s how we can approach it.

Step-by-Step Solution

First, we want to isolate the variable x. This means we need to get x by itself on one side of the equation. We can do this by following these steps:

1. Subtract 3 from both sides

To eliminate the constant term on the left side, we subtract 3 from both sides of the equation:

• 2x + 3 - 3 = 11 - 3
• This simplifies to: 2x = 8

2. Divide by 2

Next, we need to solve for x by dividing both sides by 2:

• 2x / 2 = 8 / 2
• This gives us: x = 4

Verification of the Solution

To ensure our solution is correct, we can substitute x back into the original equation:

• Original equation: 2x + 3 = 11
• Substituting x = 4: 2(4) + 3 = 8 + 3 = 11

Since both sides of the equation are equal, our solution is verified.

Understanding the Process

This method of solving equations can be applied to various types of linear equations. The key is to perform the same operation on both sides of the equation to maintain equality. Think of it like balancing a scale; whatever you do to one side, you must do to the other to keep it balanced.

Real-World Analogy

Imagine you have a box of apples, and you want to find out how many apples are in it. If you know that you have a total of 11 apples after adding 3 more, you can think of it as needing to remove those 3 apples to find out how many were originally in the box. This is similar to how we isolate x in our equation.

By following these logical steps, you can tackle a wide range of problems with confidence. Remember, practice is key to mastering these techniques, so keep working on different equations to strengthen your skills!