Download Aim #15 - Manhasset Public Schools

HW #14 Solutions: Handout
1) x > 0 and x < 3
-Infinite solutions, all real #s between 0 and 3.
-There is no absolute largest or smallest value.
-0 and 3
2) x < 1 or x ≥ 3
3) x < 2 or x > 2,
can be written as x≠2
4) x = 4 and x = 4
5)
6)
7) x = 4 or x = 3
­5
­4
­2
­3
­1
1
0
2
3
5
4
8)
­5
­4
­3
­2
­1
0
1
2
3
4
5
9) x < 2 or x = 2
­5
­4
­3
­2
­1
0
1
2
3
4
5
1) The addition property of equality is being applied since 9 is
being added to both sides of the equation.
6 3 9
2) -27x y z
4) Sometimes true
3) S = ±√1- A
C
Aim #15: How do we solve compound inequalities?
HW: Handout
2
Do Now: a. Solve w = 121, for w. Graph the solutionon a number line.
0
2
b. Solve w < 121, for w. Graph the solution on a number line and write the
solution set as a compound inequality.
0
2
c. Solve w ≥ 121, for w. Graph the solution on a number line and write the solution
set as a compound inequality.
0
Consider the compound inequality-5 < 2x + 1 < 4
a. Rewrite the inequality as a compound statement of inequality.
b. Solve each inequality for x. Then, write the solution to the compound
inequality.
c. Graph the solution set on the number line below. Describe all possible values of x.
0
d. Let's solve -5 < 2x + 1 < 4 without rewriting it and write the solution in two
different ways.
-5 < 2x + 1 < 4
Given x + 4 < 6 or x - 1 > 3
a. Solve each inequality for x. Then, write the solution to thecompound
inequality.
x + 4 < 6 or x - 1 > 3
b. Graph the solution set on the number line below and describe all possible values
of x.
0
Solve each compound inequality for x and graph the solutionon a number line.
a. x + 6 < 8 and x - 1 > -1
b. 6 ≤
x
≤ 11
2
c. 5x + 1 < 0 or 8 ≤ x-5
d. 10 > 3x - 2 or x = 4
e. x - 2 < 4 or x - 2 > 4
f. x - 2 ≤ 4 and x - 2 ≥ 4
g. 1 + x > -4 or 3x - 6 > -12
h. 1 + x > -4 or 3x - 6 < -12
i. 1 + x > 4 and 3x - 6 < -12
j. 7 ≤ -2x + 21 < 31
k. -3 <
j+2
<7
2
LET'S SUM IT UP!
"or"
The solution to a compound inequality separated by ________
should be aunion of
either
numbers included in ____________of the two solution sets.
"and"
The solution to a compound inequality separated by __________
is only thevalues
both
that are in ___________
of the individual solution sets. This should be the
intersection
___________________of
the two solution sets.
If a compound inequality is separated by "or" it is possible for the solution set to
be all real numbers. However it is not possible to have no solution.
If a compound inequality is separated by "and" it is possible to have no solution.
However it is not possible for the solution to be all real numbers.