00:01
Okay, i want to solve this inequality symbolically.
00:03
And i see automatic, what does it mean to solve it symbolically? well, i want to get x by itself and figure out how i can express x in interval notation, right? figure out all the x values that satisfy this inequality.
00:17
Okay, so i can get x by itself by performing different properties of equality, adding to both sides, subtracting to both sides, distributed property, so on and so forth.
00:27
What i see automatically is that i have fractions, and i'm not a fan of fraction, so i want to get rid of them.
00:34
So i know that in my left side, i'm dividing by four to the entire left side.
00:40
So to get rid of that fraction, opposite of dividing is going to multiply by four to both sides.
00:47
And this multiplication by four is going to be to the entire right side and left side.
00:51
So this will cancel this four.
00:53
I also see that i have a fraction of my right side.
00:56
I'm dividing the whole right side by three.
00:59
So the opposite operation of dividing is i'm going to multiply by three to both sides.
01:05
And i'm going to do this to the entire left side.
01:10
Three is cancel on the right.
01:12
Okay, so on the left side, i'll have three times the quantity one minus x.
01:17
And on the right side, i'll have four.
01:19
I can switch four and two minus x because i can multiply in any order.
01:25
Does this flip my inequality when i'm multiplied by four, and multiply by three.
01:31
Well, what flux my inequality when i'm multiply and divide by negative numbers? and there's no negative numbers here, so i'm just going to say strictly less than.
01:42
So now, order of operation, what else can i do? well, first i need to simplify what's in the parentheses.
01:50
I need to distribute to both sides.
01:51
So i'm going to distribute three to the left side.
01:56
And i'm also going to distribute four to the right side.
01:59
Okay, so three times one is three minus three...