Algebra 1 Common Core Student Edition, Grade 8-9

& G o t It? 1. NTs th e set of even n atu ral n u m b ers th a t are less th a n or equal to 12.

How do you write N in roster form? In set-builder notation?

You can use set-builder n o tatio n to w rite th e solutions of a linear inequality.

Pl q n ^
H o w is th is p ro b le m
similar to others
you've solved?
It requires using
properties of inequality
to solve a m ulti-step
inequality, as you did in
Lesson 3-4.

In equalities a n d Set-B uilder N o tatio n

Multiple Choice In set-builder notation, how do you write the solutions of

• 5x + 7 < 17?
  CE> {-2,-1,0, ...}
  CE) {x | x ^ -2 }

CA> x — —2

GD {x | x > - 2 }

—5 x + 7 < 17

—5 x + 7 - 7<17 — 7 S ub tra ct 7 fro m each side.

—5 x < 1 0 Simplify.

^ Divide each side by -5. Reverse the inequality symbol.

xS-2 Simplify.

In set-builder notation, th e solutions are given by {x | x > — 2 }. The answ er is B.

vj G ot It? 2. In set-builder notation, how do you write the solutions of 9 — 4n > 21?

W h y is th e o rig in a l
set considered a
subset?
It's a subset because it
contains elements from
the original set. In this
case, it's the subset
tha t contains all three
elements.

You know th a t a set A is a subset of a set B if each elem en t of A is also an elem en t of

B. For example, if B = { - 2 , — 1, 0,1, 2, 3} an d A = { — 1, 0, 2}, then A is a subset of B.

You can write this relationship asACB.

The em pty set, or null set, is th e set th a t contains no elem ents. The em pty set is a subset

of every set. Use 0 or { } to represent the empty set.

Finding Subsets

What are all the subsets of the set {3,4,5}?

0 Start w ith the empty set.

{ 3 }, { 4 }, { 5 } List th e subsets w ith one elem ent.

{3, 4}, {3, 5}, {4, 5} List the subsets with two elements.

{ 3 , 4, 5 } List th e o rig in a l set. It is alw ays considered a subset.

The eight subsets of {3, 4, 5 } are 0, { 3 }, { 4 }, { 5 }, {3, 4}, {3, 5}, {4, 5}, and {3,4, 5}.

.,jj) G o t It? 3. a. W hat are th e subsets of th e set P = {a, b } l Of the set S = {a, b, c}?

I b. Reasoning Let A = {x \ x < - 3 } and B = {x | x ^ 0 }. Is A a subset of B1

Explain your reasoning.

c

Po w erAlg eb ra.com 1 Lesso n 3-5 Working With Sets^195