Question

solve
–2(x – 3) ≥ 5 – (x + 3)

Answer 1

First of all, what can you do with the left side?

Answer 2

well I need to distribute the -2
so i have
-2x-3 is greater than or equal to 5-(x+3)?

Answer 3

Nope, look:
–2(x – 3)
-2*(x)-(-2)*3
-2x-(-6)
-2x+6

It should be like this, then you have

(-2x+6) ≥ 5 – (x + 3)

Answer 4

You could pass the (x+3) to the left side by adding (x+3) to both side

(-2x+6) ≥ 5 – (x + 3)
(-2x+6) + (x+3) ≥ 5

Answer 5

I am so confused on how to do this
so you multiplied the -2
then add the (x+3)? why?
how would I get to the conclusion of this?

Answer 6

-2(x – 3) ≥ 5 – (x + 3)
-2*(x)-(-2)*3
-2x-(-6)
-2x+6
(-2x+6) ≥ 5 – (x + 3)
(-2x+6) + (x+3) ≥ 5

Answer 7

-2(x – 3) ≥ 5 – (x + 3)
-2x+6>= 5-x-3
-X>=-4
x<=4

Answer 8

were u solving for x lol

Answer 9

@Supernalstudier did you understand?

Answer 10

yes I was solving for x
did you multiply the -2 to the -3?
and distribute the 5?

Answer 11

yes multiply the -2 to -3 to expand the bracket

Answer 12

jus solve as though the >= sign was = you only change its direction when u multiply both sides with a minus sign

Answer 13

–2(x – 3) ≥ 5 – (x + 3)
Let's begin step by step
First Let's evaluate the left hand side
\[-2(x-3)\]
Multiply 2 to both the terms inside the bracket
\[-(2x-6)\]
Now as we have "-" outside, change the sign of the terms inside the bracket, we get
\[-2x+6\]
Did you understand till here?

Answer 14

Thank you all so much I really need help with inequalities
I defiantly understand a little bit better and am going to try the next problem on my own

Answer 15

Great @Supernalstudier

Answer 16

one question though why did the -2 not cancel out?

Answer 17

–2(x – 3) ≥ 5 – (x + 3)
-2x+6>= 5-x-3
-X>=-4
x<=4

if you multiplied it to both sides wouldn't it cancel out?

Answer 18

-2?

Answer 19

why would u want to multiply -2 to both sides

Answer 20

you only multiply it to the -3?

does that mean I did this one wrong?
1. x – 3 > –9
+3 +3
x>-6

Answer 21

when u solve problems like that do not add to both sides
x-3>-9
x>-9 +3
x>-6

Answer 22

instead just bring them over

Answer 23

and when u bring them over to the other side the sign changes

Answer 24

@Supernalstudier you did right, We will add 3 to both sides

Answer 25

But here
\[-2(x-3)\ge 5-(x+3)\]
As we already have -2 in the inequality, we will multiply it to only the left hand side

Answer 26

This is like
\[2\times(x)=4\]
here we already have 2 on the left hand side
But I can still add, sub, multiply or divide any no. to both sides.
We use these both sides operations to get just the variable no number along with it
example
here I Have
\[2\times (x)=4\]
I have a 2 with x. I don't like it. I need to remove it
I'll divide both sides by 2 and then I'll get
\[x=2\]
So it's just x. So we always try this in any equation or inequality.

Answer 27

Did you get this?

Answer 28

I understand if you have 2x (x) =4
x=4
that one is easier
but I would use the same concept for the more complex equations?

Answer 29

Yeah it's applicable everwhere

Answer 30

thank you