Let’s assume that a is less than b. For the given inequality, the product of the two paranteses should be negative. This means the parantese would be negative when the x is less than a and the second parantese would be negative when the x is less than b. Now consider one number line that two numbers a and b are shown on that. Based on the above statement, the first and second paranteses are both negative when the x is less than a. This means the product of two numbers is positive and therefore can not be the answer because we are looking for the answer with negative products. On the other hand the two paranteses are positive when the x is more than b. This means the product of the two paranteses also in this case is positive which is rejected also. The only answer would be the one that one parantese is positive and the second one is negative. The product of two positive and negative signs would be negative. Means the x should be in between a and b. For our assumptions, a<=x<=b. For case b<a, just the location of a and b in this domain are changed.
6 years ago
Answered By Peter O
a. A is less than or equal to x less than or equal to B, xER
6 years ago
Answered By Xuezhong J
A, see drawing, x-A <=0, x-B>=0, so A <= X < = B
6 years ago
Answered By Mohsen F
Let’s assume that a is less than b. For the given inequality, the product of the two paranteses should be negative. This means the parantese would be negative when the x is less than a and the second parantese would be negative when the x is less than b. Now consider one number line that two numbers a and b are shown on that. Based on the above statement, the first and second paranteses are both negative when the x is less than a. This means the product of two numbers is positive and therefore can not be the answer because we are looking for the answer with negative products. On the other hand the two paranteses are positive when the x is more than b. This means the product of the two paranteses also in this case is positive which is rejected also. The only answer would be the one that one parantese is positive and the second one is negative. The product of two positive and negative signs would be negative. Means the x should be in between a and b. For our assumptions, a<=x<=b. For case b<a, just the location of a and b in this domain are changed.
6 years ago
Answered By Peter O
a. A is less than or equal to x less than or equal to B, xER