+23245 One way to calculate this: Find the points that make this equation true: -(7c - 18)(2c) = 0
-(7c - 18)(2c) = 0
Divide both sides by -1: (7c - 18)(2c) = 0
Either 7c - 18 = 0 or 2c = 0
7c = 18 c = 0
c = 18/7
These two points separate the number line into three sections:
the section where c < 0,
the section where 0 < c < 18/7,
the section where c > 18/7
Try a number from the section where c < 0; try any negative number (I'll pick -2) in the original problem: -(7c - 18)(2c) > 0 ---> -(7·-2 - 18)(2·-2) = -7(-32)(-4) > 0 this doesn't work!
Try a number from the section 0 < c < 18/7; I'll pick 1. -(7c - 18)(2c) > 0 ---> -(7·1 - 18)(2·1) = -7(-11)(2) > 0 this works!
Try a number from the section where c > 18/7; I'll pick 10. -(7c - 18)(2c) > 0 ---> -(7·10 - 18)(2·10) = -7(52)(20) > 0 this doesn't work!
So the solution is 0 < c < 18/7.
(If there had been a ≥ or a ≤ sign in the original problem, there would be this type of sign in the answer.
+23245 One way to calculate this: Find the points that make this equation true: -(7c - 18)(2c) = 0
-(7c - 18)(2c) = 0
Divide both sides by -1: (7c - 18)(2c) = 0
Either 7c - 18 = 0 or 2c = 0
7c = 18 c = 0
c = 18/7
These two points separate the number line into three sections:
the section where c < 0,
the section where 0 < c < 18/7,
the section where c > 18/7
Try a number from the section where c < 0; try any negative number (I'll pick -2) in the original problem: -(7c - 18)(2c) > 0 ---> -(7·-2 - 18)(2·-2) = -7(-32)(-4) > 0 this doesn't work!
Try a number from the section 0 < c < 18/7; I'll pick 1. -(7c - 18)(2c) > 0 ---> -(7·1 - 18)(2·1) = -7(-11)(2) > 0 this works!
Try a number from the section where c > 18/7; I'll pick 10. -(7c - 18)(2c) > 0 ---> -(7·10 - 18)(2·10) = -7(52)(20) > 0 this doesn't work!
So the solution is 0 < c < 18/7.
(If there had been a ≥ or a ≤ sign in the original problem, there would be this type of sign in the answer.
