Let k be a negative real number and let x and y be real numbers such that x<y. Consider the statement:
kx>ky
Answer the questions that follow.
a. (i) Is the above statement always true, always false, or does it depend on particular values of x and y? Give a logical justification.
b. (ii) Using your conclusion from part (i), explain what happens to the direction of an inequality when both sides are multiplied by the same negative number.