4.5 Compound Inequalities. 4.5 – Compound Inequalities Goals / “I can…” – Solve and graph...
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Transcript of 4.5 Compound Inequalities. 4.5 – Compound Inequalities Goals / “I can…” – Solve and graph...
4.5 – Compound Inequalities
• Goals / “I can…”– Solve and graph inequalities containing and– Solve and graph inequalities containing or
4.5 – Compound Inequalities
• A compound inequality is two inequalities joined with an and or an or.
AND (intersection)• The value for x makes BOTH inequalities true.
What is the difference between and and or?
AND means intersection-what do the two items
have in common?
OR means union-if it is in one item, it is in
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
c) Combine the graphs
●
3 42o
d) Where do they intersect?●
3 42o
2) Graph x < 2 or x ≥ 4
3 42●
a) Graph x < 2
b) Graph x ≥ 43 42
o
c) Combine the graphs
3 42o
3 42●
3 42●
3) Which inequalities describe the following graph?
-2 -1-3oo
Answer NowAnswer Now
1. y > -3 or y < -12. y > -3 and y < -13. y ≤ -3 or y ≥ -14. y ≥ -3 and y ≤ -1
When written this way, it is the same thing as 6 < m AND m < 8
It can be rewritten as m > 6 and m < 8 and graphed as previously shown, however,
it is easier to graph everything between 6 and 8!
4) Graph the compound inequality 6 < m < 8
7 86oo
5) Which is equivalent to-3 < y < 5?
1. y > -3 or y < 52. y > -3 and y < 53. y < -3 or y > 54. y < -3 and y > 5
Answer NowAnswer Now
6) Which is equivalent to x > -5 and x ≤ 1?
1. -5 < x ≤ 12. -5 > x ≥ 13. -5 > x ≤ 14. -5 < x ≥ 1
Answer NowAnswer Now
7) 2x < -6 and 3x ≥ 12
1. Solve each inequality for x
2. Graph each inequality3. Combine the graphs4. Where do they
intersect?5. They do not! x cannot
be greater than or equal to 4 and less than -3 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) Graph 3 < 2m – 1 < 9
Remember, when written like this, it is an AND problem!
3 < 2m – 1 AND 2m – 1 < 9Solve each inequality.
Graph the intersection of 2 < m and m < 5.
0 5-5
4.5 – Compound Inequalities
Writing compound inequalities:• All real numbers that are less than 31 but
greater than 25.
4.5 – Compound Inequalities
Solving compound inequalities:• (Separate the inequalities)
5 > 5 – f > 2
4.5 – Compound Inequalities
Writing OR• Discounted tickets are offered for children
under 7 or adults 65 and older.
• Graphing OR