Linear Inequalities
Common Core State Standards
A-REI.D.12 Gr ap h t h e so l u t i o n s t o a l i n ear i n eq u al i t y i n
two variables as a half-plane ... Also A-CED.A.3
MP 1, MP 2, M P 3 , MP 4, MP 6Objectives To graph linear inequalities in two variables
To use linear inequalities w h en m odeling real-w orld situationsGet t i n g Read y!Paperback H Hardcover
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books t h at you can b uy? Exp lain.One o f t h ese and
one of t hose...
no, w ait. Th r ee of
these ...MATHEMAIICAL
PRA CTI CESLesso n \
Vocabulary
linear inequalit y- solution of an
inequality
A lin e a r in e q u a lity in two variables, such as y > x - 3, can be form ed by replacing the
equal sign in a linear equation w ith an inequality symbol. A solution of an inequality
in two variables is an o rdered pair th a t m akes th e inequality true.Esse n t i a l U n d e r s t a n d i n g A linear inequality in two variables h as a n infinite
n u m b e r of solutions. These solutions can be re p resen te d in the coordinate p lan e as the
set of all points on one side of a b o u n d ary line..Think
Have you tested
solutions before?
Yes. You have tested
whether ordered
pairs are solutions of
equations. Now you w ill
te s t ordered pairs to see
w h e th e r th e y sa tisfy an
inequality.Identifying Solut ions of a Linear Inequalit y
Is th e o rd e re d p a ir a so lu tio n o f y > x — 3?0 ( 1 , 2 ) O ( — 3, — 7)
y > x - 3 <— Write the inequality. -> j/>x-3
2 i 1 - 3 *— Substitute. —* - 7 i-3 -3
2 > —2 <— Simplify. —* -7 > — 6 X
(1, 2) is a solution. ( —3, —7) is not a solution.Got It? 1. a. Is (3, 6) a solution of y < \x + 4?
b. Reasoning Suppose an o rdered p air is n o t a solution of
y > x + 10. M ust it be a solution of y < x + 10? Explain.394 Chapter 6 Systems of Equations and Inequalities