To solve a one-variable equation, undo operations in reverse order and do the same thing to both sides until x is alone, then substitute to check. Inequalities work the same way, except multiplying or dividing by a negative number flips the sign. In this free lab you choose each step and the lab applies it exactly.
Undo addition or subtraction first, then multiplication or division. For 3x + 7 = 22, subtract 7 from both sides to get 3x = 15, then divide both sides by 3 to get x = 5.
When x appears on both sides, first move the x terms to one side. For 5x + 2 = 4x + 7, subtract 4x from both sides to get x + 2 = 7, so x = 5. With parentheses, distribute first, or divide both sides by the number in front.
Substitute your answer into the original equation. If x = 5 in 3x + 7 = 22, then 3(5) + 7 = 22, so it checks. Checking takes seconds and catches sign slips.
Only when you multiply or divide both sides by a negative number. For −4x + 10 ≥ 42, subtract 10 to get −4x ≥ 32, then divide by −4 and flip: x ≤ −8. Adding or subtracting, even a negative number, never flips the sign.
Test a value to confirm the direction: x = −9 gives −4(−9) + 10 = 46, and 46 ≥ 42 is true.
Use an open circle for < or > (the boundary is not included) and a closed circle for ≤ or ≥ (it is included). Shade toward the values that make the inequality true.
Name the unknown, find the amount that changes with it and the amount charged once, then write the total. A $40 fee plus $25 a month for x months, totalling $190, is 25x + 40 = 190, so x = 6. “At most” means ≤, and “at least” means ≥.
Simplify each side (distribute and combine like terms), collect the x terms on one side, then undo addition or subtraction before multiplication or division.
Multiplying or dividing by a negative reverses the order of numbers: 2 < 3, but −2 > −3. The sign flips to keep the statement true.
No. Only multiplying or dividing both sides by a negative number flips the inequality. Adding or subtracting never does.
If you are left with a true statement such as 4 = 4, every number is a solution. If you are left with a false statement such as 4 = 7, there is no solution.
Yes. ATI says a basic on-screen calculator is built into the exam and is available on every question in every section. It adds, subtracts, multiplies and divides, and has percent, square root, decimal point, backspace and memory keys. It is not a scientific or graphing calculator, and personal, phone and watch calculators are not allowed.
Facts checked 2026-10-25. Practice items and data in this lab are original and invented; they are not real TEAS questions.
TEASPATH is independent of ATI. ATI TEAS® and TEAS® are registered trademarks of Assessment Technologies Institute, L.L.C., which is not affiliated with and does not endorse TEASPATH. Practice results are not official scores or admission predictions.
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