Question

If ax + b < ax + c is true for all real values x, what will be the solution of ax + b > ax + c ?

Can someone help please? Trying to help my daughter! Thanks!

Answer 1

Step-by-step explanation and Answer:

The inequality ax + b < ax + c is true for all real values of x if and only if b < c.

If we subtract ax from both sides of the inequality, we get b < c.

So, if b < c is true, then ax + b > ax + c has no solution because b is always less than c.

If b = c, then ax + b = ax + c for all x, and ax + b > ax + c has no solution because b and c are equal.

Therefore, the solution to ax + b > ax + c is an empty set, meaning there are no real values of x that satisfy this inequality.

Answer 2

ax + b < ax + c leads to b < c after we subtract ax from both sides.

Example: 2x+3 < 2x+4 leads to 3 < 4

Both inequalities are always true regardless of what we pick for x.

This will mean 2x+3 > 2x+4 is never true, simply because 3 > 4 is never true.

Going back to the template, it means ax+b > ax+c is never true as well.

The fact "ax + b < ax + c is true for all real values x" means all of the x values are taken, and all of the oxygen in the room is used, so there isn't any room for ax+b > ax+c to be true at all.

Answer: No solutions