Solving Linear Inequalities

Solving and graphing inequalities. In MathBound, the free Algebra I adventure game, Greater Gator asks these problems, and the only way past is to solve them.

Part of Linear Inequalities: chapter 3 of the standard course.

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

What you will practice

Graphing and Intervals. Graph a strict inequality (< or >) on a number line.
Solve using Addition/Subtraction. Solve an inequality using the addition or subtraction property.
Solve using Multiplication/Division. Solve an inequality by multiplying or dividing by a positive number.
Multi-step Inequalities. Solve a multi-step inequality with variables on one side.
Translate and Solve. Translate a basic inequality phrase and solve.

Worked examples

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

Example 1 · Graphing and Intervals

Which

describes

the

graph

of

x > 1 ?

$An$ $open$ $circle$ $at$ $1,$ $shaded$ $to$ $the$ $left$
$An$ $open$ $circle$ $at$ $1,$ $shaded$ $to$ $the$ $right$
$A$ $closed$ $circle$ $at$ $1,$ $shaded$ $to$ $the$ $left$
$A$ $closed$ $circle$ $at$ $1,$ $shaded$ $to$ $the$ $right$

Show the worked steps

$>$ $is$ $strict,$ $so$ $the$ $endpoint$ $is$ $not$ $included$ $and$ $the$ $circle$ $is$ $open.$
$x$ $is$ $greater$ $than$ $1,$ $so$ $shade$ $to$ $the$ $right.$

Answer: $An$ $open$ $circle$ $at$ $1,$ $shaded$ $to$ $the$ $right$

Example 2 · Solve using Addition/Subtraction

Solve:

x + 2 \leq 8

$x \leq - 6$
$x \geq 6$
$x \leq 10$
$x \leq 6$

Show the worked steps

$Subtract$ $2$ $from$ $both$ $sides.$ $Subtracting$ $does$ $not$ $change$ $the$ $direction.$
$x \leq 6 .$

Answer: $x \leq 6$

Example 3 · Solve using Multiplication/Division

Solve:

10 > 2 x

$x > - 5$
$x < 5$
$x > 5$
$x < - 5$

Show the worked steps

$Divide$ $both$ $sides$ $by$ $2 : 5 > x .$
$With$ $x$ $first$ $that$ $reads$ $x < 5 .$

Answer: $x < 5$

Where it is in your textbook

Textbook	Lessons
Standard course	3.1, 3.2, 3.3
Big Ideas Math Algebra 1	2.1, 2.2, 2.3, 2.4
Big Ideas Math Algebra 1 (2022)	2.1, 2.2, 2.3, 2.4
Carnegie Learning Algebra I	M2 2.3
CPM Core Connections Algebra	9.2.1, 9.2.2
CPS Skyline Algebra	4.4, 4.5, 4.6
enVision Algebra 1	1-5
enVision Algebra 1 (2024)	1-5
Eureka Math Algebra I (EngageNY)	1.10-1.11, 1.14-1.16
Glencoe Algebra 1	5-1, 5-2, 5-3
HMH Into Algebra 1	2.4
Holt McDougal Larson Algebra 1	5.1, 5.2, 5.3
Illustrative Mathematics Algebra 1	2.18-2.20
Illustrative Mathematics Algebra 1 (v.360)	4.1-4.3
Math Nation Algebra 1 (Florida B.E.S.T.)	4.1, 6.1, 6.3, 6.8
MVP Mathematics I (Integrated Math 1)	4.4, 4.5, 4.6
Open Up NC Math 1 (MVP)	4.4, 4.5, 4.6
OpenStax Elementary Algebra 2e	2.7
Pearson Algebra 1 Common Core	3-1, 3-2, 3-3, 3-4, 3-5, 3-6
Reveal Algebra 1	6-1, 6-2
SpringBoard Algebra 1	3

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