Question

solve the inequality.
-x less than or equal to 5
explain.

Answer 1

hint
-1(-1)=1

Answer 2

i just dont know how to solve it with the less than or equal sign

Answer 3

if you multiply both sides by a negative (or divide both sides by a negative) make sure you flip the direction of the inequality sign

Answer 4

just like if you have 3>2
and you multiply both sides by -1
you -3<-2

Answer 5

okay so i multiply both sides by one then?

Answer 6

so what happens when you multiply both sides by -1?

Answer 7

the hint was (-1)(-1)=1
we want just x by itself
1(-1)=-1 nothing changes there
so definitely multiplying both sides by -1

Answer 8

5<-1?

Answer 9

no you have -x<=5

Answer 10

multiply both sides of that by -1

Answer 11

oh so do i do anything else now?

Answer 12

@freckles

Answer 13

@Directrix

Answer 14

have you multiplied both sides by -1 yet
if so can i see the result

Answer 15

yeah you would get x<=-5 or 5

Answer 16

what is -1 times 5?

Answer 17

-5

Answer 18

so there is no or there

Answer 19

what happens to the direction of the inequality

Answer 20

it switches sides?

Answer 21

Recall if you have 3>2
and you decide you are going to multiply by -1 on both sides you have
-3<-2

Answer 22

yes flip the inequality sign

Answer 23

okay so then it would be x>-5

Answer 24

\[-x \le 5 \\ (-1)(-x) \ge (-1)(5) \text{ inequality sign has been flipped since we multiply/divide } \\ \text{ both sides by a negative } x \ge -5 \]

Answer 25

@Sadworld

Answer 26

are you still stuck?

Answer 27

we already have the answer

Answer 28

x is greater than or equal to -5

Answer 29

kinda like its just im not the best at math it takes me a while idk

Answer 30

which part confuses you

Answer 31

the whole thing, its like a tiny puzzle you cant figure which goes with which

Answer 32

you have \[-x \le 5 \\ \text{ to get } x \text{ by itself you need } -1(-x)=x \text{ on the left } \\ \text{ \to get that you need to multiply both sides by -1 } \\ (-1)(-x) \ge (-1)(5) \\ x \ge -5 \\ \text{ nothing else to do }\]

Answer 33

the inequality sign changes the direction

if you think back to non-variable numbers this is easy to see

Answer 34

you know -3<-2

Answer 35

if you multiply both sides by -1
you get 3>2

Answer 36

notice the inequality sign doesn't keep the same direction due to the multiplying/dividing by negative numbers on both sides