Solve Multi-Step Equation

Algebra-1

1. Fundamental Concepts

Definition: Multi-step equations are algebraic equations that require more than one operation to solve.
Operations: Common operations include addition, subtraction, multiplication, and division.
Variables: Variables represent unknown values in the equation.

2. Key Concepts

Basic Rule: $$a \cdot x + b = c$$

Isolation of Variable: To solve for $x$ , isolate it on one side of the equation.

Application: Used in various real-world scenarios such as physics, economics, and engineering.

3. Examples

Example 1 (Basic)

Problem: Solve $3x + 4 = 10$

Step-by-Step Solution:

Subtract 4 from both sides: $3x + 4 - 4 = 10 - 4$
Simplify: $3x = 6$
Divide both sides by 3: $x = 2$

Validation: Substitute $x = 2$ → Original: $3(2) + 4 = 10$ ; Simplified: $6 + 4 = 10$ ✓

Example 2 (Intermediate)

Problem: Solve $2x - 5 = 3x + 4$

Step-by-Step Solution:

Subtract $2x$ from both sides: $2x - 5 - 2x = 3x + 4 - 2x$
Simplify: $-5 = x + 4$
Subtract 4 from both sides: $-5 - 4 = x + 4 - 4$
Simplify: $x = -9$

Validation: Substitute $x = -9$ → Original: $2(-9) - 5 = 3(-9) + 4$ ; Simplified: $-18 - 5 = -27 + 4$ ✓

4. Problem-Solving Techniques

Visual Strategy: Use a flowchart to outline steps.
Error-Proofing: Double-check each step by substituting the solution back into the original equation.
Concept Reinforcement: Practice with a variety of problems to reinforce understanding.