Compound and Absolute Value Inequalities

Compound inequalities. In MathBound, the free Algebra I adventure game, Rope-Bridge Bandit 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

Compound Inequalities. Solve an "and" inequality in one step, or write one from a number line or a story.
Absolute Value Inequalities. Solve |x - h| < k.

Worked examples

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

Example 1 · Compound Inequalities

Solve:

0 < x + 5 < 10

$- 5 < x < 15$
$x < - 5$ $or$ $x > 5$
$- 5 < x < 5$
$5 < x < 15$

Show the worked steps

$Subtract$ $5$ $from$ $all$ $three$ $parts.$
$- 5 < x < 5$

Answer: $- 5 < x < 5$

Example 2 · Absolute Value Inequalities

Which

value

of

x

is

a

solution

of

∣ x - 2 ∣ < 5 ?

$7$
$3$
$- 6$
$- 3$

Show the worked steps

$- 3 < x < 7 .$
$Only$ $3$ $lies$ $in$ $that$ $range.$

Answer: $3$

Example 3 · Compound Inequalities

Solve:

8 \leq 4 x < 20

$2 < x \leq 5$
$- 5 \leq x < - 2$
$4 \leq x < 16$
$2 \leq x < 5$

Show the worked steps

$Divide$ $all$ $three$ $parts$ $by$ $4 .$
$2 \leq x < 5$

Answer: $2 \leq x < 5$

Where it is in your textbook

Textbook	Lessons
Standard course	3.4, 3.5
Big Ideas Math Algebra 1	2.5, 2.6
Big Ideas Math Algebra 1 (2022)	2.5, 2.6
Carnegie Learning Algebra I	M2 2.4, M2 4.2
CPM Core Connections Algebra	9.2.2, 10.3.3
enVision Algebra 1	1-6, 1-7
enVision Algebra 1 (2024)	1-6, 1-7
Eureka Math Algebra I (EngageNY)	1.14-1.16
Glencoe Algebra 1	5-4, 5-5
HMH Into Algebra 1	2.5, 8.3
Holt McDougal Larson Algebra 1	5.4, 5.6
Math Nation Algebra 1 (Florida B.E.S.T.)	6.2, 10.H1, 10.H2
Pearson Algebra 1 Common Core	3-6, 3-7, 3-8
Reveal Algebra 1	6-3, 6-4
SpringBoard Algebra 1	3, 4

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