Concept 1

Solve linear equations and inequalities; interpret solutions in context.

Solve the inequality or equation, then interpret the answer in context.

Core Idea

Solve the algebra first, then interpret what the result means in the situation. An inequality answer is often a range, but the context may ask for the greatest whole number in that range.

Understanding

Rule: Linear equations and inequalities are straightforward symbolically. The ACT twist is often in the wording after the algebra: maybe the answer must be a whole number, maybe it represents a maximum, or maybe the variable is not the final quantity asked for.

After solving, read the question one more time. That is where many easy points get dropped.

Step by Step

  1. Define the variable in terms of the situation.
  2. Write the equation or inequality from the wording.
  3. Solve, then translate the result back into the context.

Misconceptions

  • Using an equation when the wording calls for an inequality.
  • Forgetting that the question may ask for the greatest whole number that works.
  • Stopping after solving algebraically without checking the situation.
Question

Worked Example

A music app charges a one-time sign-up fee of $8 and $3 per month. If Maya can spend at most $23, what is the greatest number of months she can pay for?

Select an answer to see the explanation