Download Use for “null set” (no solutions)

Section 2.2 Using the Principles Together
Clearing Fractions and Decimals from an equation
If given a choice, most of us would rather work a problem in whole numbers rather than
fractions or decimals. We’re going to look at a little gimmick that will “clear the factions” from
an equations. We’re going to look at lots of examples. (It’s always a good idea to check your
answers by substituting into the original equation and simplifying.)
Practice:
1
3 5
x 
3
4 6
x 3 5
 
3 4 6
3 5

4 6
x
5
3
3
6
3x 
3.6 y  0.23 y  67.845
36 y  0.23 y  6.7
Conditional Equations – equations that are true for some values but not
others. (finite number of solutions)
4x 12  24
e.g.
Terminology
Contradictions – equations that have no solutions. (no solution)
e.g.
4x  6  4x  5
Identity – an equation that would be true for any value. (infinitely many
solutions)
e.g.
4x  6  4x  6
Linear Equations In One Variable –
e.g.
4x  6
ax =b
a0
Solution Set – set of solutions.
e.g. 2, 2
Use if the solution set is “all real numbers”
Use   for ”empty set” (no solutions)
Use
for “null set” (no solutions)
Practice:
#44)
2(3  4m)  6  48
#64) 13  (2c  2)  2(c  2)  3c
Homework
Sample
#86) 0.8  4(b  1)  0.2  3(4  b)
#107) 3 x  2  10
Homework: MLP (MyLabsPlus) and the following problems from the text.
1-6 Give the letter of the answer only.
87
Answer the questions. Give an example using numbers.
94
Assume the question means: Given that he does eliminate 3, what does he have to
do after that? Answer the why part by finishing the problem the way Joseph
started it.
97
Solve for x in a top down manner. If there are no solutions, or infinitely many
solutions, so state.
102 Same directions as for #97.
105 Same directions as for #97.
MLP problems & Quiz due _________ 8AM
Text problems due __________ 8AM