Linear Equations

Many Heart of Algebra questions such as this one will require you to accomplish the following steps: 

1. Define one or more variables that represent quantities in the question. 

2. Write one or more equations, expressions, inequalities, or functions representing the relationships described in the question. 

3. Solve the equation. 

4. Interpret the solution in terms of what the question is asking.

Solving an equation or inequality is often only part of the problem-solving process. You’ll also need to interpret the solution in the context of the question, so be sure to remind yourself of the question’s context and the meaning of the variables you solved before selecting your answer.

When the solution you arrive at doesn’t match any of the answer choices, consider if expanding, simplifying, or rearranging your solution will cause it to match an answer choice. Sometimes, this extra step is needed to arrive at the correct answer.