Compound Inequalities – Part 1 Honors Math – Grade 8.
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Compound Inequalities – Part 1 Honors Math – Grade 8
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Compound Inequality containing and Two inequalities connected by the word and form a compound inequality. A compound inequality containing “and” is true only if both inequalities are true. Its graph is the intersection of the graphs of the two inequalities. The solution must satisfy both inequalities. A compound inequality joined by the word AND is called a conjunction.
Transcript of Compound Inequalities – Part 1 Honors Math – Grade 8.
Compound Inequalities – Part 1
Honors Math – Grade 8
Get Ready for the Lesson
52h
The Mind Eraser Roller Coaster at Six Flags in Baltimore, Maryland, is an inverted steel track roller coaster. The trains are suspended underneath the tracks. To ride this coaster, you must be at least 52 inches tall and no more than 72 inches.
Write an inequality to represent this situation. Let h represent the height of the rider.
At least 52 inches and no more than 72 inches.
72hThe above inequalities can be combined into 52 < h < 72.
Compound Inequality containing and Two inequalities connected by the word and form a
compound inequality. A compound inequality containing “and” is true only if
both inequalities are true. Its graph is the intersection of the graphs of the two
inequalities. The solution must satisfy both inequalities. A compound inequality joined by the word AND is
called a conjunction.
Graph the solution set of the compound inequality. x < 3 and x > -2
Graph the 1st inequality.
x < 3
Graph the 2nd inequality.
x > -2
Find the intersection.Where do the graphs overlap?
This represents
the intersection.
The solution set is: -2 < x < 3 )3,2[
Graph the solution set of the compound inequality. p < 6 and p > 2
Graph the 1st inequality.
p < 6
Graph the 2nd inequality.
p > 2
Find the intersection.Where do the graphs overlap?
This represents
the intersection.
The solution set is: 2 < p < 6 ]3,2(
Graph the solution set of the compound inequality. -5 < x – 4 < 2
1. Express -5 < x – 4 < 2 using and. Then solve each inequality.
-1 < x
Graph the 2nd inequality.
x < 6
Find the intersection.Where do the graphs overlap?
This represents
the intersection.
The solution set is: -1 < x < 6
-5 < x – 4 and x – 4 < 2
-1 < x and x < 6
Graph the 1st inequality.
)6,1(
Graph the solution set of the compound inequality. 6 < r + 7 < 10
1. Express 6 < r + 7 < 10 using and. Then solve each inequality.
-1 < r
Graph the 2nd inequality.
r < 3
Find the intersection.Where do the graphs overlap?
This represents
the intersection.
The solution set is: -1 < r < 3
6 < r + 7 and r + 7 < 10
-1< r and r < 3
Graph the 1st inequality.
)3,1[
