Grade 9 · Math · Algebra 1

9th grade Compound inequalities: "and" and "or" worksheet

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Compound inequalities: "and" and "or"

Grade 9 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Ren solves -1 < 5 - x < 4 in a math notebook. What is the answer, written like 2 < x < 9 with the smaller number first?
Tala solves -8 ≤ -4x < 12 on paper. What is the answer, written like 2 < x < 9 with the smaller number first?
3.
Zee solves x > 2 and x > 5 on paper. Which answer is right?
- x > 5
- No solution
- 2 < x < 5
- x > 2
4.
Ari solves x < 4 or x < 9 with a pencil. Which answer is right?
- All real numbers
- x < 4
- 4 < x < 9
- x < 9
5.
Bo solves x ≤ -1 and x ≤ -6 in a math notebook. Which answer is right?
- -6 ≤ x ≤ -1
- x ≤ -6
- x ≤ -1
- No solution
6.
Esme solves x ≥ 3 or x ≥ 8 on paper. Which answer is right?
- x ≥ 8
- All real numbers
- 3 ≤ x ≤ 8
- x ≥ 3
7.
Luz solves 3x - 2 ≥ 7 and x + 5 ≤ 6 in a math notebook. What is the answer?
- No solution
- All real numbers
- 1 ≤ x ≤ 3
- x ≥ 3
8.
Milo solves 2x < 10 or x + 3 > 4 on paper. What is the answer?
- 1 < x < 5
- All real numbers
- No solution
- x < 5
Noah wonders how many integers make 3 < 2x + 1 < 13 true on paper. How many are there?
Pia wonders how many integers make -5 ≤ 3x + 1 ≤ 10 true with a pencil. How many are there?

9th grade Compound inequalities: "and" and "or" worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Compound inequalities: and, or. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can read a compound inequality from a graph, write the graph for an inequality, and test a number in it.
I can solve 3 < 2x + 1 < 11 and x + 3 < 1 or 2x > 10, and flip the signs when I divide by a negative.
I can tell when "and" gives no solution and when "or" gives all real numbers.

Standard: A-REI.B.3, A-CED.A.1

Words to know

compound inequality: Two inequalities joined by "and" or by "or".

and: A number must make both parts true: the overlap.

or: A number needs to make just one part true: both pieces together.

open / closed circle: Open: the end is not a solution. Closed: it is.

no solution: No number makes it true.

all real numbers: Every number makes it true.

Common mistakes

Your child joined two limits with "or" when both had to be true.

Your child joined two separate pieces with "and".

Your child mixed up which end is open and which is closed.

What to say

Ask: must the number fit both limits at once, or just one?

Ask: can one number be in both pieces at the same time?

Ask: does a closed circle mean the end number is included?

Questions parents ask

What is the most common mistake with compound inequalities: "and" and "or"?

Your child joined two limits with "or" when both had to be true.

How can I help my child with compound inequalities: "and" and "or"?

Ask: must the number fit both limits at once, or just one?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 1

See all Algebra 1

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