00:00The absolute value of x is less than x-3. The absolute value of x is less than 2-x. Let's find the smallest positive integer value of x that satisfies the inequality.
00:07That's what our friends are saying in our question.
00:08I'll write it down right away. The absolute value is less than x-3. The absolute value is 2-x. It needs to satisfy the inequality.
00:15Here, the easy way is to simply square both sides.
00:20When we take it this way, we can think of the first x-3 like this, friends.
00:28Since both x-3 and x are squared positive terms, what happens? Our inequality doesn't change direction.
00:34We can think of it like this: x-3 squared is less than 2-x squared.
00:40When that happens, let's make our move immediately.
00:42I'm saying that the square of the first one is less than x squared minus 2 times 3 times x plus 3 squared.
00:512 squared minus 2 times 2 times x plus x squared.
00:58Do the x-squared terms cancel each other out here? Yes, they do.
01:01What is minus 6x plus 9 less than, friends? 4 minus 4x.
01:10What happens if I put -6x here and 4x there, guys?
01:169 is less than 4. It becomes 6x minus 4x.
01:20From there, 5 is less than that. It becomes 2x.
01:23If I divide both sides by two, the multiplication and division terms will simplify.
01:27Our x is greater than 5 divided by 2, folks.
01:31In this case, if x is greater than 5/2, what is our solution set?
01:37Our infinitely open interval is 5 divided by 2.
01:42The smallest positive integer is 5 divided by 2, which is 2.5, right guys?
01:47Because it is 2 point 5.
01:48We say that the smallest positive integer x is 3.
01:543.
01:544.
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