00:01
In this problem we have to solve the given inequality.
00:04
So the inequality is here modulus 2 minus 3x greater than 5.
00:12
So since this is the modulus, so we will write a definition of modulus function.
00:18
So this is x if x greater than 0 and minus x if x is less than 0.
00:26
So, using this definition, we will take the first case, so case one, where this 2 minus 3x is greater than 0.
00:40
If 2 minus 3x greater than 0, then we can have 3x less than 2 or x less than 2 by.
00:51
Now if 2 minus 3x greater than 0, so we can write this as 2 minus 3x equal 2 minus 3x equal 2.
01:00
Minus 3x if 2 minus 3 x greater than 0 and minus 2 plus 3x if 2 minus 3x less than 0 so we will solve it if 2 minus 3 x so this 2 minus x greater than 0 then this can be written as 2 minus 3x greater than 5 so solving this we have 2 minus 5 greater than 3x.
01:37
So we have 3x is less than minus 3 or x is less than minus 1.
01:44
We have here two things.
01:46
X is less than 2 by 3 and x is less than minus 1.
01:50
Taking the intersection, the solution in this case, the solution is x is less than minus 1.
02:02
Or we can write it as x belong to minus infinity to minus one now the second case we will take this two minus x two minus three x less than zero in this case we have modulus two minus three x is minus two plus three x so case two minus three x less than zero so in this case we have x is greater than two or x is greater than 2 by 3 in this case we have the inequality minus 2 plus 3x greater than 5 or 3x greater than 7 by 3 so x is greater than 7 by 3 so x is greater than 7 by 3 we have here x is greater than 2 by 3 and x is greater than 7 by 3 the intersection of these 2 is x is greater than 7 by 3.
03:13
So in this case the solution is x belong to 7 by 3 to infinity...
