Algebra 1 Common Core Student Edition, Grade 8-9

r) Problem 3 Writing and Solving a Compound Inequality

Jhm k__
W h a t is a n o th e r w a y
to solve this problem?
You can work backward
to solve this problem.
You can start w ith the
inequality 84 < x £ 86
where x represents the
average of your test
scores. Then rewrite the
inequality in terms o f the
sum of your 4 test scores.

Test A v er ag e To earn a B in your algebra course, you must achieve an unrounded

test average between 84 and 86 , inclusive. You scored 86,85, and 80 on the first three

tests of the grading period. What possible scores can you earn on the fourth and final

test to earn a B in the course?

Know

• Test average must be between
  84 and 86, inclusive


• First 3 test scores

deed PiqQ.

Possible scores you can W rite an expression fo r your

earn on the last test to test average. Then w rite and

get a B in the course solve a compound inequality.

84 <

4(84) <

336 <

86 + 85 + 80 + x

,(2 5 L t« )

< 8 6 W rite a com pound inequality.

< 4(86) Multiply each part by 4.

251 + x < 344 Simplify.

336 -25l£ 251 +x~ 251 < 3 4 4 - 2 5 1 S u b tra c t251 fro m each part.

85 £ x <93 Simplify.

Your score o n th e fourth test m u st be b etw een 85 an d 93, inclusive.

Go t It? 3. Reasoning Suppose you scored 78, 78, an d 79 on th e first th ree tests. Is it

possible for you to ea rn a B in th e course? Assum e th at 100 is th e m axim um

grade you can ea rn in th e course an d on th e test. Explain.

H o w is th is in e q u a lity

different from others

you've solved?

It contains the word

or. Unlike an and

inequality, it's formed

by tw o inequalities w ith

solutions th a t do not

overlap.

A solution of a c o m p o u n d inequality involving or is any n u m b e r th at m akes either

inequality true. To solve a c o m p o u n d inequality involving or, you m u st solve separately

th e two inequalities th a t form th e c o m p o u n d inequality.

Solving a Compound Inequality Involving O r

What are the solutions of 3f + 2 < - 7 or — 4f + 5 < 1? Graph the solutions.

3f+2<-7 or —4 t + 5 < 1

3t + 2 — 2 < —7 — 2 or - 4 f + 5-5<l-5

3 1< —I -41< -4

3f ^ H

3 3

t< -3

or

or

or

-_4t^~4

-4 -4

t> 1

Reverse the inequality

symbol when you

divide by a negative

number.

The solutions are given byf<—3orf>l.

« I 0 F-

-4 -3 -2

g G ot It? 4. W hat are the solutions of - 2 y + 7<lor4y + 3< -5? Graph the solutions.

202 Chapter 3 So l vi n g In eq u al i t i es