Homework on Algebra
BSNS2120, J. Wang
Name ____________________
Variables X, Y, Z can take any real values.
For each true/false question, if your answer is false, then you must provide a
counter-example (i.e, give an example for which it is false).
1. 200X > –200X.
a. True
Counter Example: X=–1.
So, 200X=–200, and –200X=+200.
But (200X=–200) not> (–200X=+200).
b. False
2. X–1 < X.
a. True
b. False
Because (X-1) is always one unit to the right of X on the number line, and the
number on the left is less than the number on his right.
3. 3X > 2X.
a. True
Counter Example: X=–1.
So, 3X=-3, and 2X=–2.
But (3X=–3) not> (2X=–2).
Another counter example: X=0.
So, 3X=0, and 2X=0.
But (3X=0) not> (2X=0).
X
 1.
a. True
Y
Counter Example: X=2, Y=–1.
X
2

 2 , which is not> 1.
So,.
Y 1
Another counter example: X=0 and Y=-2.
X
0

 0 , which is not> 1.
So,.
Y 2
4. If X is greater than Y, then
b. False
b. False
5. If X>Y, then X+Z > Y+Z.
a. True
b. False
Because by adding a same amount on both sides, the original inequality still
holds.
6. If X>Y and Y>Z, then X>Z.
a. True
Because “greater than” has the transitive property.
b. False
7. If X>Z and Y>Z, then X+Y > Z.
a. True
b. False
Counter Example: X=–3, Y=–4. Z=–5.
In this example, (X=–3)>(Z=–5), and (Y=–4)>(Z=–5), so the
premise X>Z and Y>Z is satisfied.
But (X+Y=–7) not> (Z=–5).
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8. If X+Y > Z, then X>Z and Y>Z.
a. True
b. False
Counter Example: X=1, Y=4. Z=3.
In this example, (X+Y=5 which is > Z=3, so the premise is
satisfied.
But (X=1) not> (Z=3).
9. If X<=Y, then –2X _____ –2Y.
a. >=
b. <=
Because both sides are multiplied by a negative number -2.
10. If –0.5X>Y, then ___________.
a. X>0.5Y
b. X<–0.5Y
c. X>2Y
Because both sides are divided by a negative number -0.5.
d. X<–2Y
11. If X=0.4X+0.4, then X= _________. (i.e., solve the equation for X)
X – 0.4X = 0.4,
0.6X = 0.4,
X = 0.4/0.6 = 2/3.
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