00:01
So in this question, we are going to find all the values of x that satisfy at least one of the two inequalities.
00:17
Or 2x plus 1 is less than 3.
00:22
Solving on the left gives me 2x is greater than 8, which is equivalent to x is greater than 4.
00:32
Or, on the right, 2x is less than 2, subtracting 1 from each side, dividing by 2, x is, less than 1 and so what i'm getting x is greater than 4 or x is less than 1 i'm getting something that looks like this if you've seen interval notation we've got negative infinity to 1 as well as from 4 to infinity now in b we've got 2x minus 7 is less than or equals 1 or 2x plus 1 is less than 3.
01:27
So on the left, adding 8 to each side, and dividing by 2 gives you x is less than or equal to 4, while on the right, again, solving, gives you x is less than 1.
01:45
So we have x is less than or equal to 4, or x is less than one.
01:57
So x is less than one looks like this.
02:00
X is less than or equal to four looks like this and covers up that first interval.
02:09
And so what we're getting here is something like this where we just have x is less than or equal to four as our answer or in interval notation, the interval from negative infinity to positive 4.
02:26
And then third and finally, in c, we've got 2x minus 7 is less than equal to 1, or 2x plus 1 is greater than 3...