HSA.CED.A.3 math practice. Learn by doing.

HSA.CED.A.3 practice covers 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. Work through 8 free questions with answers and explanations, then continue in the related math games.

Grade 7Grade 97 mapped skills
What it covers

Skills aligned to HSA.CED.A.3

Sum of consecutive integers (ACT)

Grade 710 questions

Three integers in a given ratio (ACT)

Grade 711 questions

Compound inequality situations

Grade 910 questions

Constraints and viable solutions (SAT)

Grade 910 questions

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

Grade 910 questions

Linear system word problems (ACT/SAT)

Grade 910 questions

Writing systems from context

Grade 910 questions
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8 free questions · 0/0 correct

Practice playeasy

The sum of three consecutive odd integers is 7575. What is the largest integer?

Let the integers be nn, n+2n + 2, and n+4n + 4. Then n+(n+2)+(n+4)=75n + (n + 2) + (n + 4) = 75, so 3n+6=753n + 6 = 75, 3n=693n = 69, and n=23n = 23. The largest is n+4=27n + 4 = 27.

Practice playeasy

The sum of three numbers in the ratio 1:2:41 : 2 : 4 is 6363. What is the middle number?

Let the numbers be kk, 2k2k, and 4k4k. Then k+2k+4k=63k + 2k + 4k = 63, so 7k=637k = 63 and k=9k = 9. The middle is 2k=2(9)=182k = 2(9) = 18.

Practice playeasy

A shipping label allows a package weight ww, in pounds, that is more than 22 pounds but at most 1010 pounds. Which inequality represents the possible values of ww?

More than 22 means w>2w > 2. At most 1010 means w≤10w \le 10, so 2<w≤102 < w \le 10.

Practice playeasy

A concert sells ss student tickets and aa adult tickets. There are 22 times as many student tickets as adult tickets, and 2727 tickets are sold in all. Which system of equations represents this situation?

There are 22 times as many student tickets as adult tickets, so s=2a.s = 2a\textsf{.} In all there are 2727 tickets, so s+a=27.s + a = 27\textsf{.}

Practice playeasy

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{.}

Practice playeasy

At a cafe, burgers cost bb dollars each and fries cost ff dollars each. One order of 44 burgers and 33 orders of fries cost $30.\text{\char36}30\textsf{.} Another order of 22 burgers and 55 orders of fries cost $22.\text{\char36}22\textsf{.} What is the price of one order of fries?

The system is 4b+3f=304b + 3f = 30 and 2b+5f=22.2b + 5f = 22\textsf{.} Double the second equation: 4b+10f=44.4b + 10f = 44\textsf{.} Subtract the first: 7f=14,7f = 14\textsf{,} so f=2.f = 2\textsf{.}

Practice playeasy

Lena is ℓ\ell years old and her brother is bb years old. Lena is 22 times as old as her brother, and the sum of their ages is 3636. Which system of equations represents this situation?

Lena is 22 times as old as her brother, so ℓ=2b\ell = 2b. The sum of their ages is 3636, so ℓ+b=36.\ell + b = 36\textsf{.}

Practice playeasy

The sum of three consecutive even integers is 8484. What is the largest integer?

Let the integers be nn, n+2n + 2, and n+4n + 4. Then n+(n+2)+(n+4)=84n + (n + 2) + (n + 4) = 84, so 3n+6=843n + 6 = 84, 3n=783n = 78, and n=26n = 26. The largest is n+4=30n + 4 = 30.

Keep playing

Practice HSA.CED.A.3 inside a game.

The placement test chooses the right difficulty while every match keeps the standard in play.

Batting Cage game coverBatting CagePlay →Blaster Gate game coverBlaster GatePlay →Blitz Tanks game coverBlitz TanksPlay →Buzzer Beater game coverBuzzer BeaterPlay →
Tests that assess these skills:
LEAP 2025NAEPNC EOG/EOCACTSAT
Test reporting domains
ACT 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: AlgebraACT Aspire All grades: Preparing for Higher Math
Nearby standards
HSA.CED.A.2HSA.CED.A.4All Common Core standards