Absolute Value Equations and Inequalities

What type of compound inequality is used for | x - 2 | ≤ 4 ?

"AND" compound inequality

What type of compound inequality is used for | x + 7 | > 9 ?

"OR" compound inequality

Solve | 5n + 13 | = -7

No Solution for n

Solve | x | = -25

No Solution for x

Solve -3| y | = 9

No Solution for y

Solve | n | - 25 = -13

n = 12 , n = -12

Solve | -9n | < 54

n > -6 and n < 6

Solve | n | > 2

n > 2 or n < -2

Solve | 2n + 3 | ≤ 5

n ≤ 1 and n ≥ -4

Solve | -6n | ≤ 60

n ≤ 10 and n ≥ -10

Solve | 2n - 1 | ≥ 1

n ≥ 1 or n ≤ 0

Solve | -6w - 18 | = 24

w = 1 , w = -7

Solve 2 = | w - 13 |

w = 15 w = 11

Solve -6| w - 3 | < -24

w > 7 or w < -1

Solve 2| x + 5 | - 1 < 3

x < -3 and x > -7

Solve | 10 + 4x | < 14

x < 1 and x > -6

Solve | x + 5 | < 9

x < 4 and x > -14

Solve 2| x | = 20

x = 10 x = -10

Solve | x | = 13

x = 13 x = -13

Solve 3| x - 4 | + 21 = 27

x = 2 , x = 6

Solve | 6x | + 3 = 21

x = 3 , x = -3

Solve -4| x | = -16

x = 4 , x = -4

Solve | 4x + 1 | - 3 = 26

x = 7 , x = -7.5

Solve | 10x + 4 | > 74

x > 7 or x < -7.8

Solve | 6x + 9 | ≤ 9

x ≤ 0 and x ≥ -3

Solve | x + 3 | ≥ 7

x ≥ 4 or x ≤ -10

Solve | 4y + 11 | < 7

y < -1 and y > -4.5

Solve 5| 8 - y | = 30

y = 2 , y = -14

Solve -4| 7 + y | = -44

y = 4 , y = -18

Solve | 4y - 9 | > 27

y > 9 or y < -4.5