Radical inequalities are usually taught in Algebra 2, and this page is a preview for Algebra 1 students who can already solve square root equations. Square both sides, then solve an ordinary two-step inequality. Every question has a single square root on one side and a whole number on the other. A greater-than gives a ray such as x ≥ 11; a less-than also needs the inside to stay at zero or above, so the answer is a range like -16 ≤ x ≤ 9.
Also taught in Algebra 2, at its own level and with its own examples.
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Pick more than one for a sheet that mixes them.
The preview can look cramped on a phone. The PDF and printed sheet come out normal.
The root needs 2x - 6 ≥ 0, which is x ≥ 3, and every x ≥ 11 already meets it.
The answer is x≥11.
Where students go wrong
Forgetting to square the number on the other side. From √(2x - 6) ≥ 4 the next line is 2x - 6 ≥ 16, not 2x - 6 ≥ 4.
Also called square root inequalities, solving radical inequalities or inequalities with radicals.
Questions about these worksheets
Yes. Every radical inequalities sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the radical inequalities questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
Forgetting the lower end. x < 22 alone lets in x = -10, where the root does not exist.