Absolute Value Equations

Absolute value equations have two answers. In MathBound, the free Algebra I adventure game, Mirror Twins asks these problems, and the only way past is to solve them.

Part of Solving Linear Equations: chapter 2 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

Solve Absolute Value Equations. Solve |x - h| = k.

Worked examples

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

Example 1 · Solve Absolute Value Equations

Kai

solved

∣ x - 7 ∣ = 6

and

gave

x = 13

as

the

only

answer.

What

is

the

complete

solution?

$x = - 13$ $or$ $x = - 1$
$x = 1$ $or$ $x = 13$
$x = 13$
$x = - 13$ $or$ $x = 13$

Show the worked steps

$Kai$ $solved$ $only$ $x - 7 = 6 .$
$The$ $bars$ $also$ $equal$ $6$ $when$ $x - 7 = - 6,$ $so$ $x = 1 .$
$So$ $x = 1$ $or$ $x = 13 .$

Answer: $x = 1$ $or$ $x = 13$

Example 2 · Solve Absolute Value Equations

Solve:

2 = ∣ x + 7 ∣

$x = - 5$
$x = 2$ $or$ $x = - 2$
$x = 5$ $or$ $x = 9$
$x = - 9$ $or$ $x = - 5$

Show the worked steps

$It$ $says$ $∣ x + 7 ∣ = 2 .$
$Either$ $x + 7 = 2$ $or$ $x + 7 = - 2 .$
$So$ $x = - 9$ $or$ $x = - 5 .$

Answer: $x = - 9$ $or$ $x = - 5$

Example 3 · Solve Absolute Value Equations

Solve:

17 - 4 ∣ x - 4 ∣ = 5

$x = 7$
$x = 1$ $or$ $x = 7$
$no$ $solution$
$x = - 8$ $or$ $x = 16$

Show the worked steps

$Subtract$ $17 : - 4 ∣ x - 4 ∣ = - 12,$ $then$ $divide$ $by$ $- 4 .$
$So$ $∣ x - 4 ∣ = 3 .$
$x - 4 = 3$ $or$ $x - 4 = - 3,$ $so$ $x = 1$ $or$ $x = 7 .$

Answer: $x = 1$ $or$ $x = 7$

Where it is in your textbook

Textbook	Lessons
Standard course	2.4, 3.5
Big Ideas Math Algebra 1	1.4, 2.6
Big Ideas Math Algebra 1 (2022)	1.6, 2.6
Carnegie Learning Algebra I	M2 4.2
CPM Core Connections Algebra	3.3.1, 10.2.6, 10.3.3
enVision Algebra 1	1-7
enVision Algebra 1 (2024)	1-7
Eureka Math Algebra I (EngageNY)	3.15-3.16
Glencoe Algebra 1	2-5, 5-5
HMH Into Algebra 1	8.3
Holt McDougal Larson Algebra 1	5.5, 5.6
Math Nation Algebra 1 (Florida B.E.S.T.)	10.3, 10.4, 10.H1, 10.H2
Pearson Algebra 1 Common Core	3-7
Reveal Algebra 1	2-5, 6-4
SpringBoard Algebra 1	4

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