Solving absolute value inequalities - Absolute Value

Solving absolute value inequalities

Lessons

Notes:

$\bullet$ absolute value inequalities: $| \heartsuit |$ < $a$ ,
solution: $-a$ < $\heartsuit$ < $a$
$\bullet$ absolute value inequalities: $| \heartsuit |$ > $a$ ,
solution: $\heartsuit$ < $-a$ $\;or\;$ $\heartsuit$ > $a$

1.
Solving Basic Absolute Value Inequalities
Solve:
3.
Solving Absolute Value Inequalities Involving “greater than”
Solve:
4.
Multiplying/Dividing an Inequality by a Negative Number
Solve:
5.
Given a Pair of Inequalities, Determine the Corresponding Absolute Value Inequality
Determine the absolute value inequality statement that corresponds to each inequality:
6.
Recognizing Absolute Value Inequalities with “No Solution” or “All Real Numbers”
Solve:

Solving absolute value inequalities

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Intro Lesson:

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Lesson: 1a

Lesson: 1b

Lesson: 2

Lesson: 3a

Lesson: 3b

Lesson: 4a

Lesson: 4b

Lesson: 5a

Lesson: 5b

Lesson: 6a

Lesson: 6b

Intro

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Lessons

Notes:

∙ \bullet ∙ absolute value inequalities: ∣♡∣ | \heartsuit |∣♡∣ < aaa, solution:−a-a−a < ♡\heartsuit♡ < aaa ∙ \bullet ∙ absolute value inequalities: ∣♡∣ | \heartsuit |∣♡∣ > aaa, solution:♡\heartsuit♡ < −a-a−a or\;or\;or ♡\heartsuit♡ > aaa

Intro Lesson

1.

Solving Basic Absolute Value Inequalities Solve:

a)

∣x∣ |x| ∣x∣ < 444 ∣x∣≤|x| \leq∣x∣≤ 444

b)

∣x∣ |x| ∣x∣ > 444 ∣x∣≥ |x| \geq∣x∣≥ 444

2.

Solving Absolute Value Inequalities Involving “less than” Solve: ∣2x−1∣ |2x-1|∣2x−1∣ < 333

3.

Solving Absolute Value Inequalities Involving “greater than” Solve:

a)

∣4x−5∣ |4x-5| ∣4x−5∣ > 777

b)

∣x∣−5≥−1 |x|-5 \geq -1∣x∣−5≥−1

4.

Multiplying/Dividing an Inequality by a Negative Number Solve:

a)

∣3−2x∣≤11 |3-2x| \leq 11 ∣3−2x∣≤11

b)

∣−x6+53∣ |-\frac{x}{6}+\frac{5}{3}| ∣−​6​​x​​+​3​​5​​∣ > 222

5.

Given a Pair of Inequalities, Determine the Corresponding Absolute Value Inequality Determine the absolute value inequality statement that corresponds to each inequality:

a)

−1-1 −1 < xxx < 555

b)

x≤−10 x \leq-10x≤−10 or\;or\;or x≥2x \geq 2x≥2

6.

Recognizing Absolute Value Inequalities with “No Solution” or “All Real Numbers” Solve:

a)

∣x+3∣ |x+3| ∣x+3∣ < −5-5−5

b)

∣x−4∣ |x-4| ∣x−4∣ > −1-1−1

Solving absolute value inequalities

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

or

$\bullet$ absolute value inequalities: $| \heartsuit |$ < $a$ ,
solution: $-a$ < $\heartsuit$ < $a$
$\bullet$ absolute value inequalities: $| \heartsuit |$ > $a$ ,
solution: $\heartsuit$ < $-a$ $\;or\;$ $\heartsuit$ > $a$

Solving Basic Absolute Value Inequalities
Solve:

$|x|$ < $4$
$|x| \leq$ $4$

$|x|$ > $4$
$|x| \geq$ $4$

Solving Absolute Value Inequalities Involving “less than”
Solve: $|2x-1|$ < $3$

Solving Absolute Value Inequalities Involving “greater than”
Solve:

$|4x-5|$ > $7$

$|x|-5 \geq -1$

Multiplying/Dividing an Inequality by a Negative Number
Solve:

$|3-2x| \leq 11$

$|-\frac{x}{6}+\frac{5}{3}|$ > $2$

Given a Pair of Inequalities, Determine the Corresponding Absolute Value Inequality
Determine the absolute value inequality statement that corresponds to each inequality:

$-1$ < $x$ < $5$

$x \leq-10$ $\;or\;$ $x \geq 2$

Recognizing Absolute Value Inequalities with “No Solution” or “All Real Numbers”
Solve:

$|x+3|$ < $-5$

$|x-4|$ > $-1$