Solve: |2x + 3| -1 < 4
2 answers:
Add 1
|2x +3| < 5
Unfold
-5 < 2x +3 < 5
Subtract 3
-8 < 2x < 2
Divide by 2
-4 < x < 1
The solution is
-4 < x < 1
_____
If you subtract 4 from both sides, you get an expression that compares to zero. Most graphing calculators will show you the zero-crossings, so you can easily find the values of x where this is true.
|2x +3| < 5
Unfold
-5 < 2x +3 < 5
Subtract 3
-8 < 2x < 2
Divide by 2
-4 < x < 1
The solution is
-4 < x < 1
_____
If you subtract 4 from both sides, you get an expression that compares to zero. Most graphing calculators will show you the zero-crossings, so you can easily find the values of x where this is true.
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Answer:
When we have a set of N elements, the number of combinations of K elements (such that N ≤ K) from these N elements is:
Then if we have 8 different types of carpet, and we want to see how many different samples of 3 types we can choose, we just need to replace N by 8, and K by 3 in the above equation:
So there are 56 different samples.
Now we can do the same, but this time we want to use 5 types of carpet, then we will have K = 5.
Again, we have 56 different samples.