Free Printable ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

1.

|v + 8| − 5 = 2

a)

{-1,-15}

b)

{-1,-5}

c)

{-15,15}

d)

No Solution

2.

|2a - 10| = 6

a)

a = 8, a = 5

b)

a = 2

c)

a = 8

d)

a = 8, a = 2

3.

Solve:
|x + 3| > 8

a)

x > 5 or x < -11

b)

x > 5

c)

all real numbers

d)

no solution

4.

| 2w - 1 | < 11

a)

No Solution

b)

All Real Numbers

c)

-5 < w < 6

d)

-6 < w < 5

5.

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

a)

n > 1 or n < -7

b)

n > -1 or n < -7

c)

-7 < n < -1

d)

no solution

6.

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

a)

no solution

b)

x > 2 or x < -22

c)

-22 < x < 2

d)

all real numbers

7.

4|5x-2|+7>39

a)

-6/5 < x > 2

b)

x=2 or x=-6/5

c)

x=2 and x=-6/5

d)

x < -6/5 or x > 2

8.

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

a)

-14

b)

-4

c)

{-14, -4}

d)

no solution

9.

| x + 3 | ≤ 2

a)

No Solution

b)

All Real Numbers

c)

-5 ≤ x ≤ -1

d)

1 ≤ x ≤ 5

10.

| 3c - 5 | < -2

a)

No Solution

b)

All Real Numbers

c)

1 < c < ⁷/₃

d)

c < 1 or c > ⁷/₃

11.

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.

a)

Between 12.18 mm and 12.30 mm, inclusive.

b)

Between 11.28 mm and 12.38 mm, inclusive.

c)

Between 12.28 mm and 12.33 mm, inclusive.

d)

Between 12.10 mm and 12.35 mm, inclusive.

12.

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.

a)

$64\ \frac{11}{25}\le w\le65\ \frac{8}{25}$

b)

$65\ \frac{1}{25}\le w\le65\ \frac{6}{25}$

c)

$64\ \frac{21}{25}\le w\le65\ \frac{16}{25}$

d)

$64\ \frac{19}{25}\le w\le65\ \frac{6}{25}$

13.

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.

a)

$\left|w-20\right|\le0.04;\ 19.96\le w\le20.04.$

b)

$\left|w-20\right|\ge0.04;\ 19.96\ge w\ge20.04.$

c)

$\left|w-0.04\right|\le20;\ 19.96\le w\le20.04.$

d)

$\left|w-20\right|<0.04;\ 19.96<w<20.04.$

14.

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?

a)

$\left|t-12\right|=23;\ \min:\ 11ºF\ and\ Max:\ 35ºF$

b)

$\left|t+23\right|=12;\ \min:\ 11ºF\ and\ Max:\ 35ºF$

c)

$\left|t-23\right|=12;\ \min:\ 11ºF\ and\ Max:\ 35ºF$

d)

$\left|t+12\right|=23;\ \min:\ 11ºF\ and\ Max:\ 35ºF$

15.

Solve

\frac{\left|x\right|}{-3}=-9.6

a)

x=-28.8 or x = 28.8

b)

x=-28.5 or x = 28.5

c)

x= 28.8

d)

No solution

16.

Solve

13\left|x-2\right|+12>9\left|x-2\right|+15

a)

$\left(-\infty,-\frac{5}{4}\right)U\left(\frac{11}{4},\ \infty\right)$

b)

$\left(-\infty,\frac{5}{4}\right)U\left(\frac{11}{4},\ \infty\right)$

c)

$\left(-\infty,-\frac{11}{4}\right)U\left(\frac{5}{4},\ \infty\right)$

d)

No solution

17.

Solve

8\left|2x-5\right|-10<4\left|2x-5\right|+15

a)

$-\ \frac{5}{8}<x<\ \frac{45}{8}$

b)

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

c)

$-\ \frac{5}{8}<x<\ \frac{41}{8}$

d)

No solution

ABSOLUTE VALUE EQUATIONS AND INEQUALITIES

Total questions: 17

Worksheet time: 4hrs 15mins

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