Grade 9 · Algebra & functions

Compound inequality situations practice

Compound inequality situations 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 compound inequality situations problems our math games drill.

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Sample questions

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Question 1easy

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.

Question 2easy

During exercise, a target heart rate hh, in beats per minute, is greater than 6060 and less than 100100. Which inequality represents the possible values of hh?

Greater than 6060 and less than 100100 are both strict, so 60<h<10060 < h < 100.

Question 3easy

On a certain road, traffic cameras record speeds ss, in miles per hour, that are at least 2525 mph and no more than 5555 mph. Which inequality represents the possible values of ss?

At least 2525 and no more than 5555 include both endpoints, so 25≤s≤5525 \le s \le 55.

Question 4easy

Cold storage requires a temperature tt, in degrees Fahrenheit, above 3232°F and below 4040°F. Which inequality represents the possible values of tt?

Above 3232 and below 4040 are both strict, so 32<t<4032 < t < 40.

Question 5easy

A car rental allows a trip length dd, in days, that is at least 22 days but less than 77 days. Which inequality represents the possible values of dd?

At least 22 gives d≥2d \ge 2. Less than 77 gives d<7d < 7, so 2≤d<72 \le d < 7.

Question 6medium

A pass/fail exam awards credit when the score ss is more than 7070 points but at most 100100 points. Which inequality represents the possible passing scores?

More than 7070 means s>70s > 70. At most 100100 means s≤100s \le 100, so 70<s≤10070 < s \le 100.

Question 7medium

A hiking trail is open only at elevations ee, in meters, from 500500 meters through 1,2001{,}200 meters, inclusive. Which inequality represents the possible values of ee?

From 500500 through 1,2001{,}200, inclusive, means both endpoints are included: 500≤e≤1,200500 \le e \le 1{,}200.

Question 8medium

A science lab classifies a liquid as neutral when its pH level pp is more than 66 but at most 88. Which inequality represents the possible values of pp?

More than 66 means p>6p > 6. At most 88 means p≤8p \le 8, so 6<p≤86 < p \le 8.

Tests that cover compound inequality situations:
SATNAEPACTLEAP 2025NC EOG/EOC
More Grade 9 skills:
Problem solving in context (SAT)Common factor factoring (SAT)Discriminant analysisInterpreting data displaysStatistics basicsAbsolute value equationsConditional probabilityEquivalent rational expressions (SAT)All Grade 9 practice →

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