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

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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

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ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

|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

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ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

|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

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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