+612 How many integers $n$ satisfy both of the inequalities $4n + 3 < 25$ and $-7n + 5 < 24$?
+983 We first need to simplify both inequalities.
4x + 3 < 25
Subtracting 3 from both sides:
4x < 22
Dividing both sides by 4:
x < 11/2
-7n + 5 < 24
Adding both sides by 7n and subtracting both sides by 24 (to avoid dividing by a negative number):
7n > -19
Dividing both sides by 7:
n > -19/7
n must be greater than -2 and -5/7 but also smaller than 5 and 1/2
The integers in between are:
-2, -1, 0, 1, 2, 3, 4, and 5
There are 8 integers
+983 We first need to simplify both inequalities.
4x + 3 < 25
Subtracting 3 from both sides:
4x < 22
Dividing both sides by 4:
x < 11/2
-7n + 5 < 24
Adding both sides by 7n and subtracting both sides by 24 (to avoid dividing by a negative number):
7n > -19
Dividing both sides by 7:
n > -19/7
n must be greater than -2 and -5/7 but also smaller than 5 and 1/2
The integers in between are:
-2, -1, 0, 1, 2, 3, 4, and 5
There are 8 integers
