Solving Algebraic Problems

Before you can solve problems using algebra, you need to become familiar with the vocabulary of algebra. For example, you need to know what variables, coefficients, terms, algebraic expressions and equations are. You should also know how to translate a statement into an equation.

Furthermore, you should understand general methods for solving equations, such as how to balance an equation. In other words, you should be familiar with transforming equations to form equivalent equations. Lastly, you will need to be able to validate a solution by evaluating an algebraic expression.

To solve for the value of an unknown in a mathematical problem, follow these 5 steps:

1. Define the variables

2. Write the equation

3. Solve the equation 

4. Verify the solution

5. Give a complete answer

To define the variables and write the equation, it is often helpful to visually represent the situation using a drawing, diagram or table. These 2 steps are crucial: you must have the correct equation to find the right answer to the problem!

Solving an equation means finding the value of the variable that makes the equation true. To do so, you must isolate the variable on one side of the equation.

Verifying your solution is a good habit to develop. It allows you to continue working on your problem with confidence. It's an opportunity to examine your solution by answering the following questions:

• Is it realistic?

• Does it respect the magnitude of the problem?

• Is the answer a decimal or a negative number, when you’re looking for a natural number?

In other words, this step should not be ignored. It allows you to develop your critical thinking as it applies to mathematical logic.

Lastly, giving a complete answer doesn't necessarily mean writing a complete sentence. What it does mean is that you need to go back and re-read the question to make sure you've answered it correctly. Sometimes, the value found in Step 3 is not the correct answer. If you don't go back and read the question, you risk overlooking it, even if the result of your calculations was correct!