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

Quiz

•

Mathematics

•

7th - 9th Grade

•

Practice Problem

•

Medium

•

CCSS

HSA.REI.B.3, 8.EE.C.7, HSA.REI.A.1

+2

Standards-aligned

Francisco Artuz

Used 19+ times

FREE Resource

17 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

|v + 8| − 5 = 2

{-1,-15}

{-1,-5}

{-15,15}

No Solution

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

2.

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.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.B.3

3.

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.CED.A.1

CCSS.HSA.REI.B.3

4.

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

| 2w - 1 | < 11

No Solution

All Real Numbers

-5 < w < 6

-6 < w < 5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

5.

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.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

6.

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

7.

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.CED.A.1

CCSS.HSA.REI.B.3

Create a free account and access millions of resources

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

12 questions

Fórmula general ecuaciones cuadráticas

Quiz

•

9th Grade

15 questions

Absolute Value and Integers

Quiz

•

6th - 7th Grade

15 questions

Year 10 Solving Equations

Quiz

•

9th - 11th Grade

13 questions

Lekcja14 7-8

Quiz

•

7th - 8th Grade

20 questions

การอธิฐานส่วน ม.1

Quiz

•

7th Grade

20 questions

Mastering Positive and Negative Integers

Quiz

•

7th Grade

14 questions

Quiz 1° medio

Quiz

•

8th Grade

18 questions

Teorem Pythagoras

Quiz

•

7th Grade

Popular Resources on Wayground

5 questions

This is not a...winter edition (Drawing game)

Quiz

•

1st - 5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

10 questions

Identify Iconic Christmas Movie Scenes

Interactive video

•

6th - 10th Grade

20 questions

Christmas Trivia

Quiz

•

6th - 8th Grade

18 questions

Kids Christmas Trivia

Quiz

•

KG - 5th Grade

11 questions

How well do you know your Christmas Characters?

Lesson

•

3rd Grade

14 questions

Christmas Trivia

Quiz

•

5th Grade

20 questions

How the Grinch Stole Christmas

Quiz

•

5th Grade

Discover more resources for Mathematics

10 questions

Identify Iconic Christmas Movie Scenes

Interactive video

•

6th - 10th Grade

15 questions

Solving Equations with Variables on Both Sides Review

Quiz

•

8th Grade

20 questions

Solving Systems of Equations by Graphing

Quiz

•

8th Grade

15 questions

Christmas Movie Trivia

Quiz

•

7th Grade

25 questions

Christmas Trivia

Quiz

•

8th Grade

20 questions

Scatter Plots and Line of Best Fit

Quiz

•

8th Grade

12 questions

8th U4L11 On Both of the Lines

Quiz

•

8th Grade

33 questions

Algebra 1 Semester 1 Final 2025

Quiz

•

8th - 10th Grade

ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

17 questions

|v + 8| − 5 = 2

|2a - 10| = 6

Solve:
|x + 3| > 8

| 2w - 1 | < 11

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

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

4|5x-2|+7>39

Evaluate each expression.
| x + 9 | = -5

| x + 3 | ≤ 2

| 3c - 5 | < -2

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

17 questions

|v + 8| − 5 = 2

|2a - 10| = 6

Solve: |x + 3| > 8

| 2w - 1 | < 11

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

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

4|5x-2|+7>39

Evaluate each expression.| x + 9 | = -5

| x + 3 | ≤ 2

| 3c - 5 | < -2

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Solve:
|x + 3| > 8

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

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

Evaluate each expression.
| x + 9 | = -5