Algebra
Lesson 6-1
Vocabulary:
Set-Builder Notation- A concise way of writing a solution set. For example, {t|<58} represents the set of all numbers y such that y is less than 17.
Addition Property of Inequality- If any number is added to each side of a true inequality, the resulting inequality is also true.
Subtraction- If any number is subtracted from each side of a true inequality, the resulting inequality is also true.
Examples:
Solve the following inequality. Then graph it on a number line.
c+9 < 3
•First, get the variable on one side alone. To do that, minus 9 from each side.
•When you minus 9 from 9, you are left with zero, or just C on that side.
•When you minus 9 from 3, you are left with -6 on the other side.
•So, you end up getting c < -6
Solve this inequality, and graph if on a number line:
x-24 > 54
+24 +24
x > 78
Solve this equation:
y+6 < 18
-6 -6
y < 12
Solve this equation:
3-x < 4
-3 -3
-x < 1 Divide so you dont have a negative variable
-1 -1
-3 -3
-x < 1 Divide so you dont have a negative variable
-1 -1
answer: x < -1
y + 5 > 12
y + 5 - 5 > 12 - 5
y + 5 - 5 > 12 - 5
y + 0 > 12 - 5
y > 7
Solve
x-8>16
+8 +8 Add 8 to both sides to get the variable by itself.
x>24
Solve and graph
c-4+2<6+3
c-2<9 Combine like terms.
+2 +2 Add 2 to both sides to get the variable by itself once again.
c<11 Remember it is an open circle because it isn't an "...or equal to"
Additional Information:
•You can graph an inequality on a number line.
•If the greater than or less than sign has a "_" under it, (<,>), then the circle on the number line will be filled in. If it doesn't
have a "_" under it, then the circle remains open.
•The arrow will point the way the number line is supposed to point, as long as the variable comes first. (> = ----->)
Online resources:
http://www.glencoe.com/sec/math/algebra/algebra1/algebra1_05/extra_examples/chapter6/lesson6_1.pdf This website has some great examples.
http://www.purplemath.com/modules/ineqsolv.htm
Another website with some information on inequalities.
Another website with some information on inequalities.
Pictures:
This page by: DRV, Amanda Tate C.J.H. CK D.A.S.