Model relationships with equations/inequalities and translate word problems into algebra.
Translate each part of a word problem into algebra before you solve.
Core Idea
Translate the relationship sentence by sentence. One phrase usually gives the variable meaning, another gives the total, and words like at least or at most tell you whether you need an inequality.
Understanding
Rule: Word problems get easier when you stop trying to convert the whole paragraph at once. Define the variable first, then map each sentence to one algebra statement.
On ACT, the common misses are not algebra mistakes. They are translation mistakes: mixing up total and rate, reversing who has more, or using an equation when the wording actually creates an inequality.
Step by Step
- Define the variable first.
- Translate each sentence into one algebra statement.
- Choose an equation or inequality that matches the wording.
Misconceptions
- Using the variable for the wrong quantity.
- Reversing a comparison such as "5 more than twice x."
- Writing an equation when the context says at least or at most.
Worked Example
Student tickets to a play cost
Select an answer to see the explanation