Question

find the solution of the inequality
|x - 5| ≥ 3

Answer 1

take x-5 and 5-x >= 3

Answer 2

this is equivalent to

x - 5 >= 3 and x - 5 <= -3

solve these 2 inequalities and you have it

Answer 3

can you solve
x - 5 >= 3 ?

Answer 4

do you know what the | | (= ' mod' ) around an expression means ?

Answer 5

absolute value

Answer 6

it means x-5 can be either positive or negative. so take (x-5) and -(x-5)

Answer 7

okay

Answer 8

thats why you have 2 possibilities

Answer 9

leading to 2 equations

Answer 10

2 different answers?

Answer 11

the answers will be a range of values of x - i should have said 2 inequalities

x - 5 >= 3
x >= 8

-now solve the other inequality

Answer 12

yes, because it depends on wheter the original equation was positive or negtive. its like multiple roots of a quadratic, there can be more than 1

Answer 13

x <= -8

Answer 14

@cwrw238

Answer 15

no

x <= -3 + 5

Answer 16

add 5 to both sides of the inequality

Answer 17

x <= 2?

Answer 18

right

Answer 19

so combining these 2 results we have

x <=2 or x >= 8

Answer 20

thanks

Answer 21

and we can graph it on a number line as follows