The ideal diameter of a gear for a certain type of clock is 12.24 mm. An actual diameter can vary by 0.06 mm. Find the range of acceptable diameters.

Between 12.18 mm and 12.30 mm, inclusive.

Between 11.28 mm and 12.38 mm, inclusive.

Between 12.28 mm and 12.33 mm, inclusive.

Between 12.10 mm and 12.35 mm, inclusive.

The ideal width of a certain conveyor belt for a manufacturing plant is 65 in.An actual conveyor belt can vary from the ideal by at most 6/25 in. Find the acceptable widths for this conveyor belt.

64 19 25 ≤ w ≤ 65 6 25 64\ \frac{19}{25}\le w\le65\ \frac{6}{25} 6 4 2 5 1 9 ≤ w ≤ 6 5 2 5 6

64 11 25 ≤ w ≤ 65 8 25 64\ \frac{11}{25}\le w\le65\ \frac{8}{25} 6 4 2 5 1 1 ≤ w ≤ 6 5 2 5 8

65 1 25 ≤ w ≤ 65 6 25 65\ \frac{1}{25}\le w\le65\ \frac{6}{25} 6 5 2 5 1 ≤ w ≤ 6 5 2 5 6

64 21 25 ≤ w ≤ 65 16 25 64\ \frac{21}{25}\le w\le65\ \frac{16}{25} 6 4 2 5 2 1 ≤ w ≤ 6 5 2 5 1 6

A pasta manufacturer makes 20-oz boxes of macaroni. The manufacturer knows that not every box weighs exactly 20-oz. the allowable difference is 0.04-oz. Write and solve an absolute value inequality that represents this situation.

∣ w − 20 ∣ ≤ 0.04 ; 19.96 ≤ w ≤ 20.04. \left|w-20\right|\le0.04;\ 19.96\le w\le20.04. ∣ w − 2 0 ∣ ≤ 0 . 0 4 ; 1 9 . 9 6 ≤ w ≤ 2 0 . 0 4 .

∣ w − 20 ∣ ≥ 0.04 ; 19.96 ≥ w ≥ 20.04. \left|w-20\right|\ge0.04;\ 19.96\ge w\ge20.04. ∣ w − 2 0 ∣ ≥ 0 . 0 4 ; 1 9 . 9 6 ≥ w ≥ 2 0 . 0 4 .

∣ w − 0.04 ∣ ≤ 20 ; 19.96 ≤ w ≤ 20.04. \left|w-0.04\right|\le20;\ 19.96\le w\le20.04. ∣ w − 0 . 0 4 ∣ ≤ 2 0 ; 1 9 . 9 6 ≤ w ≤ 2 0 . 0 4 .

∣ w − 20 ∣ < 0.04 ; 19.96 < w < 20.04. \left|w-20\right|<0.04;\ 19.96<w<20.04. ∣ w − 2 0 ∣ < 0 . 0 4 ; 1 9 . 9 6 < w < 2 0 . 0 4 .

A meteorologist reported that the previous day's temperatures varied 12º from normal temperature of 23ºF. Write an absolute value equation and find, what were the maximum and minimum temperatures possible on the previous day?

∣ t − 23 ∣ = 12 ; min ⁡ : 11 º F a n d M a x : 35 º F \left|t-23\right|=12;\ \min:\ 11ºF\ and\ Max:\ 35ºF ∣ t − 2 3 ∣ = 1 2 ; min : 1 1 º F a n d M a x : 3 5 º F

∣ t − 12 ∣ = 23 ; min ⁡ : 11 º F a n d M a x : 35 º F \left|t-12\right|=23;\ \min:\ 11ºF\ and\ Max:\ 35ºF ∣ t − 1 2 ∣ = 2 3 ; min : 1 1 º F a n d M a x : 3 5 º F

∣ t + 23 ∣ = 12 ; min ⁡ : 11 º F a n d M a x : 35 º F \left|t+23\right|=12;\ \min:\ 11ºF\ and\ Max:\ 35ºF ∣ t + 2 3 ∣ = 1 2 ; min : 1 1 º F a n d M a x : 3 5 º F

∣ t + 12 ∣ = 23 ; min ⁡ : 11 º F a n d M a x : 35 º F \left|t+12\right|=23;\ \min:\ 11ºF\ and\ Max:\ 35ºF ∣ t + 1 2 ∣ = 2 3 ; min : 1 1 º F a n d M a x : 3 5 º F

Solve 13 ∣ x − 2 ∣ + 12 > 9 ∣ x − 2 ∣ + 15 13\left|x-2\right|+12>9\left|x-2\right|+15 1 3 ∣ x − 2 ∣ + 1 2 > 9 ∣ x − 2 ∣ + 1 5

( − ∞ , 5 4 ) U ( 11 4 , ∞ ) \left(-\infty,\frac{5}{4}\right)U\left(\frac{11}{4},\ \infty\right) ( − ∞ , 4 5 ) U ( 4 1 1 , ∞ )

( − ∞ , − 5 4 ) U ( 11 4 , ∞ ) \left(-\infty,-\frac{5}{4}\right)U\left(\frac{11}{4},\ \infty\right) ( − ∞ , − 4 5 ) U ( 4 1 1 , ∞ )

( − ∞ , − 11 4 ) U ( 5 4 , ∞ ) \left(-\infty,-\frac{11}{4}\right)U\left(\frac{5}{4},\ \infty\right) ( − ∞ , − 4 1 1 ) U ( 4 5 , ∞ )

Solve 8 ∣ 2 x − 5 ∣ − 10 < 4 ∣ 2 x − 5 ∣ + 15 8\left|2x-5\right|-10<4\left|2x-5\right|+15 8 ∣ 2 x − 5 ∣ − 1 0 < 4 ∣ 2 x − 5 ∣ + 1 5

− 5 8 < x < 45 8 -\ \frac{5}{8}<x<\ \frac{45}{8} − 8 5 < x < 8 4 5

5 8 < x < 45 8 \ \frac{5}{8}<x<\ \frac{45}{8} 8 5 < x < 8 4 5

− 5 8 < x < 41 8 -\ \frac{5}{8}<x<\ \frac{41}{8} − 8 5 < x < 8 4 1

ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Authored by Francisco Artuz

Mathematics

7th - 9th Grade

CCSS covered

Used 19+ times

ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

AI Actions

Add similar questions

Adjust reading levels

Convert to real-world scenario

Translate activity

More...

Content View

Student View

17 questions

Show all answers

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

|v + 8| − 5 = 2

{-1,-15}

{-1,-5}

{-15,15}

No Solution

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.REI.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

|2a - 10| = 6

a = 8, a = 5

a = 2

a = 8

a = 8, a = 2

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Solve:
|x + 3| > 8

x > 5 or x < -11

x > 5

all real numbers

no solution

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

| 2w - 1 | < 11

No Solution

All Real Numbers

-5 < w < 6

-6 < w < 5

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Solve.
-5|4 +n| < -15

n > 1 or n < -7

n > -1 or n < -7

-7 < n < -1

no solution

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Solve.
| -x - 10| + 4 < -8

no solution

x > 2 or x < -22

-22 < x < 2

all real numbers

Tags

CCSS.HSA.REI.B.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

4|5x-2|+7>39

-6/5 < x > 2

x=2 or x=-6/5

x=2 and x=-6/5

x < -6/5 or x > 2

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Microsoft

or continue with

Facebook

Apple

Others

Already have an account?

Similar Resources on Wayground

20 questions

Factorización: Trinomio x^2+bx+c

Quiz

•

9th Grade

20 questions

LATIHAN SOAL 1

Quiz

•

9th Grade

20 questions

1.0 INDEKS Tingkatan 3

Quiz

•

KG - Professional Dev...

15 questions

Compare and order Rational Numbers H.W

Quiz

•

8th Grade

16 questions

Actividad 11: Multiplicación de signos

Quiz

•

9th Grade

14 questions

Un bon départ - Calcul littéral 5ème

Quiz

•

1st - 10th Grade

13 questions

Znaky dělitelnosti 2

Quiz

•

6th - 9th Grade

20 questions

Penilaian Harian Ke- 1 Materi Bilangan Berpangkat dan Bentuk Akar

Quiz

•

9th Grade

Popular Resources on Wayground

11 questions

Hallway & Bathroom Expectations

Quiz

•

6th - 8th Grade

10 questions

HCS SCI 03 Summer School Assessment 2

Quiz

•

3rd Grade

11 questions

Home Scope

Quiz

•

7th - 8th Grade

12 questions

2026 TAP Technology in the Classroom

Presentation

•

Professional Development

15 questions

HCS SCI 05 Summer School Assessment 2 Review

Quiz

•

5th Grade

15 questions

HCS SCI 04 Summer School Review 2

Quiz

•

4th Grade

59 questions

Geometry Unit 3 Review

Quiz

•

9th - 12th Grade

14 questions

FAST ELA READING SMAPLE TEST MATERIALS

Passage

•

3rd Grade

Discover more resources for Mathematics

59 questions

Geometry Unit 3 Review

Quiz

•

9th - 12th Grade