Heart of Algebra

Linear Inequalities

Solve linear inequalities and interpret solution sets on the number line. Each question below has a complete worked solution.

This collection of 25 SAT math practice questions on linear inequalities is sequenced by difficulty so you can warm up on routine problems and progress to the kind of question that separates a competitive math score from an elite one. The first eight problems are calibrated to roughly easy College Board difficulty — the kind that appears in the first third of the math section. The next ten are medium difficulty: the bread-and-butter of the middle of the test. The final seven push into hard territory, where the question writers add an extra step, hide a sign change, or ask for an unrelated expression after you solve.

Work each question on paper before you look at the worked solution. The solution is there to confirm or correct your work, not to lead you. If you cannot start a problem after 30 seconds, mark it and come back; if you cannot finish after 90 seconds, look at the first line of the solution and try again. That structured exposure to the worked solution — not a glance, not a copy — is the most reliable way to convert a missed question into a permanent skill.

#QuestionDifficultyBand
1 Which of the following describes all values of x for which -7x - 7 > -7? easy 400-500 Open
2 Which of the following describes all values of x for which 8x + 7 > 7? easy 400-500 Open
3 Which of the following describes all values of x for which 3x + 10 > -20? easy 400-500 Open
4 Which of the following describes all values of x for which -6x - 8 > -2? easy 400-500 Open
5 Which of the following describes all values of x for which 7x + 1 > 15? easy 400-500 Open
6 Which of the following describes all values of x for which 7x + 1 > 15? easy 400-500 Open
7 Which of the following describes all values of x for which -7x + 9 > -5? easy 500-600 Open
8 Which of the following describes all values of x for which 6x + 0 > 0? easy 500-600 Open
9 Which of the following describes all values of x for which 8x + 9 > 17? medium 500-600 Open
10 Which of the following describes all values of x for which -8x - 2 > -10? medium 500-600 Open
11 Which of the following describes all values of x for which 8x - 10 > -18? medium 500-600 Open
12 Which of the following describes all values of x for which 4x + 2 > -14? medium 500-600 Open
13 Which of the following describes all values of x for which -2x - 4 > 12? medium 600-700 Open
14 Which of the following describes all values of x for which 2x - 8 > -18? medium 600-700 Open
15 Which of the following describes all values of x for which 3x - 10 > 11? medium 600-700 Open
16 Which of the following describes all values of x for which -7x - 6 > -6? medium 600-700 Open
17 Which of the following describes all values of x for which 5x + 9 > 9? medium 600-700 Open
18 Which of the following describes all values of x for which 7x - 8 > -15? medium 600-700 Open
19 Which of the following describes all values of x for which -8x - 9 > -9? hard 600-700 Open
20 Which of the following describes all values of x for which 5x + 6 > 1? hard 700-800 Open
21 Which of the following describes all values of x for which 3x + 1 > -8? hard 700-800 Open
22 Which of the following describes all values of x for which -7x + 3 > 3? hard 700-800 Open
23 Which of the following describes all values of x for which 5x + 7 > 17? hard 700-800 Open
24 Which of the following describes all values of x for which 7x - 5 > 2? hard 700-800 Open
25 Which of the following describes all values of x for which -4x + 3 > -9? hard 700-800 Open