Overlap RollerArrowfolk · inequalities

Two paint rollers whose stripes overlap: systems of inequalities.

Systems of Linear Inequalities

Systems of inequalities. In MathBound, the free Algebra I adventure game, Overlap Roller asks these problems, and the only way past is to solve them.

Part of Systems of Equations and Inequalities: chapter 6 of the standard course.

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Verify Solutions.
Solve by Graphing. Graph a system of two inequalities and identify the overlapping shaded region as the solution set.
Applications. Translate a word problem with multiple constraints into a system of inequalities and graph the viable region.

Made by the game’s own question engine. Try each one, then open its steps.

Is

(4, 14)

a

solution

of

the

system

y > 3 x + 3

and

y < 4 x + 1 ?

Show the worked steps

$At$ $x = 4 :$ $the$ $first$ $needs$ $y > 15$ $and$ $the$ $second$ $needs$ $y < 17 .$
$y = 14 .$
$No,$ $it$ $satisfies$ $only$ $the$ $second$ $inequality .$

Answer: $No,$ $it$ $satisfies$ $only$ $the$ $second$ $inequality$

Is

(3, 3)

a

solution

of

the

system

y > 2 x - 2

and

y < 3 x ?

Show the worked steps

Answer: $No,$ $it$ $satisfies$ $only$ $the$ $second$ $inequality$

A

student

can

work

at

most

25

hours

a

week

at

two

jobs

paying

$12

and

$17

an

hour,

and

needs

at

least

$150 .

Does

working

5

hours

at

the

first

job

and

13

at

the

second

meet

both

conditions?

Show the worked steps

$Hours:$ $5 + 13 = 18,$ $against$ $at$ $most$ $25 .$
$Pay:$ $12 (5) + 17 (13) = 281,$ $against$ $at$ $least$ $150 .$ $So:$ $Yes,$ $it$ $meets$ $both$ $conditions .$

Answer: $Yes,$ $it$ $meets$ $both$ $conditions$

Textbook	Lessons
Standard course	6.6
Big Ideas Math Algebra 1	5.7
Big Ideas Math Algebra 1 (2022)	5.7
Carnegie Learning Algebra I	M2 3.4, M2 3.6
CPM Core Connections Algebra	9.4.1, 9.4.3
CPS Skyline Algebra	5.1, 5.5-5.6
enVision Algebra 1	4-5
enVision Algebra 1 (2024)	4-5
Eureka Math Algebra I (EngageNY)	1.24
Glencoe Algebra 1	6-6
HMH Into Algebra 1	10.2
Holt McDougal Larson Algebra 1	6.6
Illustrative Mathematics Algebra 1	2.24-2.26
Illustrative Mathematics Algebra 1 (v.360)	4.7-4.9
Math Nation Algebra 1 (Florida B.E.S.T.)	6.9, 6.10
MVP Mathematics I (Integrated Math 1)	5.2, 5.5, 5.6
Open Up NC Math 1 (MVP)	5.2, 5.5, 5.6
OpenStax Elementary Algebra 2e	5.6
Pearson Algebra 1 Common Core	6-6
Reveal Algebra 1	7-5
SpringBoard Algebra 1	18