Lesson: Solving Multi-Step Equations

Objective

Learn how to solve multi-step equations involving variables on both sides.

Key Concepts

• An equation is a statement that two expressions are equal.
• To solve an equation, isolate the variable on one side.
• Use inverse operations to simplify the equation.

Steps to Solve Multi-Step Equations

1. Simplify both sides of the equation if necessary (distribute, combine like terms).
2. Move the variable terms to one side and the constant terms to the other side.
3. Isolate the variable by using inverse operations (addition/subtraction and multiplication/division).

Example

Solve the equation:

$$3x + 4 = 10$$

Step 1: Subtract 4 from both sides

$$3x + 4 - 4 = 10 - 4\ 3x = 6$$

Step 2: Divide both sides by 3

$$\frac{3x}{3} = \frac{6}{3}\ x = 2$$

Key Questions

• What is the first step when solving a multi-step equation?
• How do you handle variables on both sides of the equation?
• Why is it important to perform the same operation on both sides of the equation?

Practice Problems

1. Solve: $2x + 5 = 15$
2. Solve: $4x - 2 = 3x + 5$

Conclusion

Solving multi-step equations requires careful manipulation of both sides of the equation. Practice will help you become proficient in isolating variables and finding solutions.