How to Solve Word Problems of Algebraic Expressions

Word problems involving algebraic expressions require a systematic approach to analyze the given information, identify the unknowns, and use algebraic techniques to find the solution. Here is a step-by-step guide to solving word problems of algebraic expressions:

Step 1: Read and Understand the Problem
Carefully read the problem and understand the information provided. Identify the known quantities, unknown variables, and the relationships between them.

Step 2: Define Variables
Assign variables to the unknown quantities in the problem. Use letters (usually x, y, z) to represent these variables.

Step 3: Translate the Problem into Equations or Inequalities
Express the given information in terms of equations or inequalities using the defined variables. Pay attention to keywords that indicate mathematical operations such as "sum," "difference," "product," or "quotient."

Step 4: Solve the Equations or Inequalities
Use algebraic techniques such as simplification, factoring, distributing, or solving equations to find the solution. Apply the appropriate operations to isolate the variable on one side of the equation.

Step 5: Check the Solution
After obtaining a solution, substitute the value back into the original problem to ensure it satisfies all the given conditions. Verify that the solution makes sense in the context of the problem.

Step 6: Communicate the Solution
Present the solution in a clear and concise manner, including the value of the variable(s) and any relevant units of measurement. Provide a logical explanation of the solution and how it relates to the original problem.

Example: Finding Value
Problem: The sum of two consecutive even numbers is 42. Find the numbers.

Step 1: Read and Understand the Problem
The problem states that the sum of two consecutive even numbers is 42.

Step 2: Define Variables
Let x represent the first even number, and x + 2 represent the next consecutive even number.

Step 3: Translate the Problem into Equations or Inequalities
The sum of two consecutive even numbers is 42:
x + (x + 2) = 42

Step 4: Solve the Equations or Inequalities
Combine like terms:
2x + 2 = 42
Subtract 2 from both sides:
2x = 40
Divide both sides by 2:
x = 20

Step 5: Check the Solution
Substitute the value of x back into the original equation:
20 + (20 + 2) = 42
42 = 42 (The equation is true)

Step 6: Communicate the Solution
The two consecutive even numbers are 20 and 22.

Example: Number Patterns
Problem: Find the next three terms in the pattern: 3, 6, 9, 12, ...

Step 1: Read and Understand the Problem
The pattern consists of consecutive numbers that increase by 3 each time.

Step 2: Define Variables
No variables are needed for this problem.

Step 3: Translate the Problem into Equations or Inequalities
No equations or inequalities are required.

Step 4: Solve the Equations or Inequalities
Since it is a number pattern, we can simply continue