These are original practice items written to the HESI A2 blueprint (4 options, no penalty for wrong answers), not actual exam questions. Try each one before you open the answer.
Mathematics: Basic Algebra sits inside the Mathematics section of the HESI A2. Our bank holds 38 verified items tagged to it, and the 4 below are a fixed sample so the page stays the same every time you open it. Each one shows the reasoning, not just the letter.
The topic tag comes from our own items rather than from a published syllabus, so treat it as a map of what we cover. For the official section breakdown see the HESI A2 page.
Question 1
Solve for x: 2(x + 3) - 4 = 3x + 1.
Correct answer: B
Distribute: 2x + 6 - 4 = 3x + 1 → 2x + 2 = 3x + 1. Subtract 2x from both sides: 2 = x + 1. Subtract 1: x = 1.
Why the other options are wrong:
A: 0 might come from forgetting to distribute the 2 or incorrectly moving terms.
C: -1 would result from an error in combining like terms or sign mistakes.
D: 2 might come from adding instead of subtracting after isolating x.
Question 2
Solve for x: 2(x + 3) = 5x - 9
Correct answer: C
Expand: 2x + 6 = 5x - 9. Subtract 2x: 6 = 3x - 9. Add 9: 15 = 3x. Divide by 3: x = 5.
Why the other options are wrong:
A: Plugging x=6 gives 2(9)=18 and 5(6)-9=21, not equal.
B: Plugging x=3 gives 2(6)=12 and 5(3)-9=6, not equal.
D: Plugging x=9 gives 2(12)=24 and 5(9)-9=36, not equal.
Question 3
A nurse mixes a 20% saline solution with a 40% saline solution to obtain 10 liters of a 32% saline solution. How many liters of the 20% solution are used?
Correct answer: B
Let x = liters of 20% solution; then (10‑x) = liters of 40% solution. Equation: 0.20x + 0.40(10‑x) = 0.32×10. Simplify: 0.2x + 4 – 0.4x = 3.2 → –0.2x = –0.8 → x = 4.
Why the other options are wrong:
A: 2 liters would give a very low final concentration.
C: 6 liters of 20% would give a final concentration lower than 32% if the rest is 40% (6×0.2 + 4×0.4 = 1.2+1.6=2.8, target 3.2).
D: 8 liters would give a final concentration lower than 32% (8×0.2 + 2×0.4 = 1.6+0.8=2.4).
Question 4
A nurse needs to prepare a 2% cleaning solution from 500 mL of a 10% solution. How much water must be added? (Assume volumes are additive.)
Correct answer: A
The amount of cleaning agent in the original solution is 10% of 500 mL = 50 mL. In the final 2% solution, this 50 mL must represent 2% of the total volume. So total volume = 50 / 0.02 = 2500 mL. Water added = 2500 – 500 = 2000 mL. Alternatively, set up equation: 0.10(500) = 0.02(500 + x), solve for x = 2000.
Why the other options are wrong:
B: 1500 mL would give a total volume of 2000 mL, making the concentration 50/2000 = 2.5%, not 2%.
C: 1000 mL would give a total volume of 1500 mL, making the concentration 50/1500 ≈ 3.33%, too high.
D: 2500 mL is the final total volume, not the amount of water added.
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