solving compound inequalities. domain: a-rei reasoning with equations & inequalities cluster: 1....
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Solving Compound Inequalities
Domain: A-REI Reasoning with Equations & Inequalities
Cluster: 1. Understand solving equations as a process of reasoning and explain the reasoning.
Standard 1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Domain: A-REI Reasoning with Equations & Inequalities
Cluster: 2. Solve equations and inequalities in one variable.
Standard: 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
What is the difference between “and” and “or”?
AND means intersection-only elements common to
both sets are part of the solution.
OR means union-Elements from both sets
are part of the solution.
A
A B
B
1. Graph x < 4 and x ≥ 2
3 42●
a) Graph x < 4
b) Graph x ≥ 23 42
o
●
3 42o
c) Where do they intersect?
●3 42
o
2. Graph x < 2 or x ≥ 4
3 42●
a) Graph x < 2
b) Graph x ≥ 43 42
o
c) Unite the graphs
3 42o
3 42●
3. Which inequalities describe the following graph?
A. y > -3 or y < -1B. y > -3 and y < -1
C. y ≤ -3 or y ≥ -1D. y ≥ -3 and y ≤ -1
-2 -1-3oo
Can also be written as:
-3 < y < -1
4. Graph the compound inequality 6 < m < 8
7 86oo
“6 is less than m and m is less than 8”
6 7 8
6 7 8
o
o
“m is between 6 and 8”
5. Which is equivalent to-3 < y < 5?
A. y > -3 or y < 5B. y > -3 and y < 5C. y < -3 or y > 5D. y < -3 and y > 5
0 5-3oo
6. Which is equivalent to x > -5 and x ≤ 1?
A. -5 < x ≤ 1B. -5 > x ≥ 1C. -5 > x ≤ 1D. -5 < x ≥ 1
o0 1-5
7. Solve: 2x < -6 and 3x ≥ 12
1. Solve each inequality
1. Graph each solution
1. Where do they intersect?
1. They do not! No Solution!!
2 6
2 2 3
x
x
3x 12
3 3 x 4
-3 0-6o-3 0-6o
4 71o●4 71o●
8. Solve:3x+2 < 2 or 1-x ≥ 4
0 5-3
0 1-1o
-3 -2-4●
Unite the two sets
o ●
10. Graph x > -1 or x < 3
The entire number line is shaded!!
What is the solution???
All Real Numbers
0 3-1
10. Solve: 3 < 2m – 1 < 9
0 5-5
See Next Slide for Different Method.
Find the intersectionof the two sets.
10. Method 2:
0 5-5