Solving and interpreting inequalities in one or two variables, including flipping the inequality sign and identifying solution regions.
38
Total questions
15
Easy
13
Medium
10
Hard
Inequality questions test the same solving skills as equations plus two extra ideas: the inequality sign flips when you multiply or divide by a negative, and solutions are regions rather than points. Two-variable versions ask which point satisfies an inequality (or a system of them), or how a shaded graph region corresponds to the algebra.
For one-variable questions, solve like an equation and watch the sign at every negative multiply/divide. For two-variable questions, the fastest reliable move is testing points — plug the candidate point into the inequality and check. For word problems ("at least," "no more than"), translate the phrase to the symbol before doing anything else.
Straight from the Grind1600 question bank — try each one before revealing the answer.
Correct answer: C
Choice C is correct. Substituting (1, 2) into the inequality gives 7(1) - 4(2) = 7 - 8 = -1, and -1 < 10 is a true statement. Substituting (3, 6) into the inequality gives 7(3) - 4(6) = 21 - 24 = -3, and -3 < 10 is a true statement. Substituting (4, 3) into the inequality gives 7(4) - 4(3) = 28 - 12 = 16, and 16 < 10 is not a true statement. Therefore, (1, 2) and (3, 6) are the only ordered pairs shown that satisfy the given inequality.
Choice A is incorrect because the ordered pair (3, 6) also satisfies the inequality.
Choice B is incorrect because the ordered pair (1, 2) also satisfies the inequality.
Choice D is incorrect because the ordered pair (4, 3) does not satisfy the inequality since 16 is not less than 10.
Correct answer: A
Choice A is correct. The van can carry at most 3,200 pounds. It will also carry a 450-pound generator. Therefore, the crates can weigh at most 3,200 - 450 = 2,750 pounds. Since x represents the number of 60-pound crates and y represents the number of 80-pound crates, the total weight of crates is 60x + 80y. This must be less than or equal to 2,750 pounds: 60x + 80y ≤ 2,750.
Choice B is incorrect. This represents hauling at least 2,750 pounds of crates.
Choice C is incorrect. This doesn't account for the 450-pound generator.
Choice D is incorrect. This represents hauling at least 3,200 pounds of crates without accounting for the generator.
Linear Equations in One Variable
Solving equations of the form ax + b = c, including equations with variables on both sides, fractions, and no-solution or infinite-solution cases.
Linear Equations in Two Variables
Working with equations like y = mx + b: interpreting slope and intercepts, converting between forms, and connecting equations to their graphs.
Linear Functions
Modeling real situations with linear functions — constant rates of change, initial values, and evaluating or interpreting f(x) in context.
Systems of Linear Equations
Solving pairs of linear equations by substitution or elimination, and reasoning about when systems have one, none, or infinitely many solutions.
38 Linear Inequalities questions with step-by-step explanations, woven into a day-by-day study plan built for your test date.
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