Linear inequality situations (ACT/SAT/PSAT 8/9/10). Game on.

Linear inequality situations (ACT/SAT/PSAT 8/9/10) is a grade 9 math skill aligned to Common Core standard HSA.CED.A.3: represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 linear inequality situations (act/sat/psat 8/9/10) problems our math games drill.

CCSS HSA.CED.A.310 questions in the bank
Kickoff

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Warm-upeasy

The minimum value of ww is 1212 less than twice another number n.n\textsf{.} Which inequality shows the possible values of w?w\textsf{?}

A minimum means ww must be at least that value, so use ≥.\ge\textsf{.} Twice nn minus 1212 is 2n−12,2n - 12\textsf{,} giving w≥2n−12.w \ge 2n - 12\textsf{.}

Mid-gameeasy

The minimum value of pp is 66 more than 44 times another number k.k\textsf{.} Which inequality shows the possible values of p?p\textsf{?}

A minimum means pp must be at least that value, so use ≥.\ge\textsf{.} Four times kk plus 66 is 4k+6,4k + 6\textsf{,} giving p≥4k+6.p \ge 4k + 6\textsf{.}

Mid-gameeasy

The maximum value of hh is 22 less than 55 times another number d.d\textsf{.} Which inequality shows the possible values of h?h\textsf{?}

A maximum means hh can be at most that value, so use ≤.\le\textsf{.} Five times dd minus 22 is 5d−2,5d - 2\textsf{,} giving h≤5d−2.h \le 5d - 2\textsf{.}

Mid-gameeasy

The sum of xx and yy is less than 15.15\textsf{.} Which inequality shows the possible values of xx and y?y\textsf{?}

Less than 1515 means the sum is strictly below 15,15\textsf{,} so x+y<15.x + y < 15\textsf{.}

Mid-gamemedium

The maximum value of cc is 1515 more than 77 times another number n.n\textsf{.} Which inequality shows the possible values of c?c\textsf{?}

A maximum means cc can be at most that value, so use ≤.\le\textsf{.} Seven times nn plus 1515 is 7n+15,7n + 15\textsf{,} giving c≤7n+15.c \le 7n + 15\textsf{.}

Mid-gamemedium

The minimum value of tt is 33 less than twice another number m.m\textsf{.} Which inequality shows the possible values of t?t\textsf{?}

A minimum means tt must be at least that value, so use ≥.\ge\textsf{.} Twice mm minus 33 is 2m−3,2m - 3\textsf{,} giving t≥2m−3.t \ge 2m - 3\textsf{.}

Mid-gamemedium

Twice a number nn is no more than 18.18\textsf{.} Which inequality shows the possible values of n?n\textsf{?}

Twice nn is 2n.2n\textsf{.} No more than 1818 means 2n≤18.2n \le 18\textsf{.}

Buzzer beatermedium

The maximum value of xx is 77 less than 44 times another number y.y\textsf{.} Which inequality shows the possible values of x?x\textsf{?}

A maximum means xx can be at most that value, so use ≤.\le\textsf{.} Four times yy minus 77 is 4y−7,4y - 7\textsf{,} giving x≤4y−7.x \le 4y - 7\textsf{.}

Overtime

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Tests that cover linear inequality situations (act/sat/psat 8/9/10):
PSAT 8/9SATNAEPLEAP 2025NC EOG/EOC
Reporting domains for this skill
SAT All grades: AlgebraACT All grades: Integrating Essential SkillsSTAAR Algebra I: Linear Functions, Equations, and InequalitiesMAP Growth Math 6+: Operations and Algebraic ThinkingSBAC High School: Concepts and ProceduresNAEP Grade 12: Algebra
More Grade 9 skills
Linear inequalitiesLinear inequality system solutionsLinear graph translationsLinear-quadratic graph intersections (ACT)Linear functions from tables (ACT/SAT)Linear raise total earningsLinear equation from two points (SAT)Linear rule from a function table (ACT)All Grade 9 practice →

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