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Algebra 2 - "OR" Compound Inequalities

13 questions

10th - 12th Grade

Mathematics

Algebra 2 - “OR” Compound Inequalities is a free printable mathematics worksheet for students in Grades 10–12. It includes 13 multiple-choice questions focused on solving compound inequalities joined by OR, writing inequalities from number-line graphs, and identifying how OR solutions are represented. Students also review open and closed endpoint conventions and determine whether an inequality uses <, >, ≤, or ≥. The worksheet gives students repeated practice isolating the variable in each branch of an OR statement, reversing an inequality when multiplying or dividing by a negative, and selecting the solution set that matches a graph. It is useful for Algebra II instruction, guided practice, independent review, or an assessment of compound-inequality fluency. The worksheet is available as a free printable PDF and includes a complete answer key for efficient checking.

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Worksheets

Algebra 2 - "OR" Compound Inequalities

Total questions: 13

Name
Class
Date
1.

3x - 4 < -13 or 7x + 1 > 22

a)

x < -6 or x > 4

b)

x > 3 or x > -9

c)

x < 3 or x > -3

d)

x < -3 or x > 3

2.
Write an inequality for Graph 3.
a)
x ≤ -2 AND x > 5
b)
x ≤ -2 OR x > 5
c)
x ≥ -2 OR x < 5
d)
-2 ≤ x < 5
3.

x + 2 < -4 or -5x < -15

a)

x > -6 or x < 3

b)

x < -3 or x > 6

c)

x < -6 or x > 3

d)

x < -4 or x > 5

4.
When graphing the solutions to "OR" inequalities, The shading looks like___
a)
Shading that connects the 2 dots
b)
Shading that points away and never crosses.
c)
Shading that points toward each other and ALWAYS crosses
d)
Shading that points opposite, but sometimes crosses.
5.

2(x+4) < -8 or -3x + 4 < x - 4

a)

x > -8 or x > 2

b)

x < -8 or x < 2

c)

x < -8 or x > 2

d)

x < -8 and x < 2

6.

What inequality is graphed?

a)

x > 2 and x ≤ -3

b)

x > 2 and x < -3

c)

x ≤ -3 or x > 2

d)

x > 2 or x < -3

7.
Solve:  
3x + 2 < -4  or  4x + 4 > 24
a)
x < -2  or  x > 5 
b)
x < 2  or  x > 5
c)
x < -2  and  x > 5 
d)
x < 2  and  x > 5
8.

Write an inequality for Graph 1.

a)

x < -2 or x > 5

b)

x > -2 OR x > 5

c)

x ≥ -2 OR x < 5

d)

-2 ≤ x < 5

9.
When you graph an inequality, you used a closed dot when you use which symbols?
a)
≤, ≥ 
b)
<, >
10.
When graphing an inequality, you use an open dot when you use which symbol?
a)
<, >
b)
≤, ≥ 
11.
a)

(-∞, 2]

b)

[-4, ∞)

c)

(-∞, -4] or (2, ∞)

d)

(-∞, -4] or [4, ∞)

12.
a)

[-∞,-2] or [-2, ∞]

b)

(-∞, -2] or [-2, ∞)

c)

(-∞,2]

d)

(-∞, -4] or [4, ∞)

13.
-8<2(x+4) or -3x+4>x-4
a)
No solutions
b)
x<-8 or x<2
c)
 x>-8 or x<2
d)
x<-8 and x<2
Answer Key

Algebra 2 - "OR" Compound Inequalities

Total questions: 13

1.
d)

x < -3 or x > 3

2.
b) x ≤ -2 OR x > 5
3.
c)

x < -6 or x > 3

4.
b) Shading that points away and never crosses.
5.
c)

x < -8 or x > 2

6.
c)

x ≤ -3 or x > 2

7.
a) x < -2  or  x > 5 
8.
a)

x < -2 or x > 5

9.
a) ≤, ≥ 
10.
a) <, >
11.
c)

(-∞, -4] or (2, ∞)

12.
b)

(-∞, -2] or [-2, ∞)

13.
b) x<-8 or x<2

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FAQs

What does this OR compound inequalities worksheet cover?

This Grade 10–12 Algebra II worksheet uses 13 multiple-choice questions to practice solving compound inequalities joined by OR and matching solution sets to number-line graphs. Students isolate the variable in each inequality, handle sign reversals when dividing by a negative, identify open or closed endpoints, and recognize that OR solutions are shown as two regions extending away from the boundary points.

How can I use this worksheet to teach OR compound inequalities?

Begin by modeling one item that requires solving both inequalities separately, then combine the two results with OR and sketch the corresponding number line. Use the graph-to-inequality questions to connect notation with visual representations, asking students to explain why the solution regions point away from each other and why a boundary is open or closed. Finish with the multiple-choice items as guided practice or independent application.

What mistakes should I watch for when students complete this worksheet?

Watch for students reversing an inequality incorrectly—or failing to reverse it—when dividing by a negative, as in the items involving -5x or -3x. Students may also select AND instead of OR, connect the shaded regions, or confuse open dots for < and > with closed dots for ≤ and ≥. The graph-based questions can reveal whether they understand both endpoint notation and the direction of each shaded ray.

How do I assign and grade this OR compound inequalities worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, so you can assign the 13 multiple-choice items in the format that fits your lesson. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable option can also support schools that are reducing screen time.

How does this worksheet help students connect OR inequalities to their graphs?

Several questions require students to write an inequality from a displayed graph or identify the graph of an OR inequality, rather than only solve symbolically. These items reinforce that OR creates two solution regions, that the regions typically point away from one another, and that open or closed dots communicate whether each endpoint is excluded or included.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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