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Math · Elementary Algebra

Hard Elementary Algebra Drill

15 hard-difficulty ACT Math questions on Elementary Algebra. Each question is on its own page with a worked answer explanation, the underlying rule, and a quick study tip.

Hard Math Elementary Algebra

All 15 questions

  1. 1 Solving a Linear Equation If 4x + 7 = 31, what is the value of x? Hard
  2. 2 Multiplying Binomials (FOIL) Expand and simplify: (2x + 1)(1x + 2). Hard
  3. 3 Evaluating an Algebraic Expression If x = 4, what is the value of 3x^2 + 3x? Hard
  4. 4 Solving a Linear Inequality Solve for x: 3x + 1 > 6. Hard
  5. 5 Solving a Linear Equation If 5x + 7 = 22, what is the value of x? Hard
  6. 6 Multiplying Binomials (FOIL) Expand and simplify: (2x + 3)(1x + 2). Hard
  7. 7 Evaluating an Algebraic Expression If x = 4, what is the value of 2x^2 + 3x? Hard
  8. 8 Solving a Linear Inequality Solve for x: 4x + 1 > 16. Hard
  9. 9 Solving a Linear Equation If 5x + 3 = 28, what is the value of x? Hard
  10. 10 Multiplying Binomials (FOIL) Expand and simplify: (2x + 3)(2x + 4). Hard
  11. 11 Evaluating an Algebraic Expression If x = 4, what is the value of 3x^2 + 2x? Hard
  12. 12 Solving a Linear Inequality Solve for x: 2x + 1 > 8. Hard
  13. 13 Solving a Linear Equation If 5x + 3 = 28, what is the value of x? Hard
  14. 14 Multiplying Binomials (FOIL) Expand and simplify: (2x + 2)(2x + 2). Hard
  15. 15 Evaluating an Algebraic Expression If x = 2, what is the value of 2x^2 + 2x? Hard

How to use this drill

Open the questions one at a time. Read the prompt, decide on an answer before scrolling, then check the explanation. The point of a drill is not to "get the question right" — it's to internalize the rule so you can apply it cold under timed conditions on test day.

If you're missing more than a third of the questions in this set, drop down a difficulty tier and rebuild from there. If you're getting all of them quickly, jump up a tier and try a mixed drill across subtopics.

What "Hard" means here

Hard questions are designed to separate strong test-takers. They typically require multiple rules applied in sequence, or careful elimination among answers that all look plausible. Expect to see these appear later in real ACT sections; even strong test-takers miss a couple per test.

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