(c)x= (−5/4)y− 2
(d)x= (−5/4)y+ 2
(e) More information is necessary to answer this
- Here are several things we can do to “smaller than or equal” statements and still have
valid statements. Something is wrong with one of these claims. Which claim is wrong,
and how can it be corrected?
- We can reverse the left and right sides only if we change the inequality to “larger than
or equal.”
- We can add the same quantity to both sides.
- We can subtract the same quantity from both sides.
- We can add one statement to another.
- We can multiply both sides by the same quantity.
(a) The first statement is wrong. We can never reverse the left and right sides of any
inequality.
(b) The second statement is wrong. We can only add the same quantity to both sides
of a “smaller than or equal” statement if that quantity is positive.
(c) The third statement is wrong. We can only subtract the same quantity from both
sides of a “smaller than or equal” statement if that quantity is negative.
(d) The fourth statement is wrong. We cannot, in general, add one “smaller than or
equal” statement to another.
(e) The fifth statement is wrong. It works if the quantity is nonnegative; but if we
multiply both sides by a negative quantity, we must change the relation to “larger
than or equal.”
- In Cartesian three-space, the equation 2x+ 4 y− 6 z= 7 represents
(a) a straight line.
(b) a flat plane.
(c) a parabola.
(d) a circle.
(e) None of the above.
- Consider the following first-degree equation in the variable x, where a,b,c,d,e, and f
are constants:
− 3 a+x/(bcd)= 24 ef
This equation has meaning only under certain conditions. Which of these statements
fully states those conditions?
(a) We cannot let b,c, and d all equal 0 at the same time.
(b) We cannot allow b,c, or d to equal 0 at any time.
(c) We cannot allow a to equal 0 at any time.
Final Exam 569
