Lesson: Solving Equations

In this lesson, we will explore how to solve equations. An equation is a mathematical statement that asserts the equality of two expressions.

What is an Equation?

An equation consists of two expressions separated by an equals sign ($=$). For example, $2x + 3 = 7$ is an equation.

Steps to Solve an Equation

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

1. Identify the equation: Start with the equation you want to solve.
2. Isolate the variable: Use inverse operations to get the variable alone on one side.
3. Simplify: Perform any calculations needed to simplify the expression.
4. Check your solution: Substitute your solution back into the original equation to verify.

Example

Let's solve the equation:
$2x + 3 = 7$

Step 1: Subtract 3 from both sides: $2x + 3 - 3 = 7 - 3$
This simplifies to:
$2x = 4$

Step 2: Divide both sides by 2: $\frac{2x}{2} = \frac{4}{2}$
This simplifies to:
$x = 2$

Step 3: Check your solution: Substituting $x = 2$ back into the original equation: $2(2) + 3 = 7$
This simplifies to: $4 + 3 = 7$
Since this is true, our solution is correct!

Key Questions

• What steps do you follow to isolate the variable in an equation?
• How can you verify your solution?
• What are inverse operations, and why are they important?

Keywords

• Equation
• Variable
• Isolate
• Inverse Operations
• Solution