Algebra 1 Common Core Student Edition, Grade 8-9

Think
You can use reasoning
and guess-and-check
to solve th e problem. If
either 9 o r 10 is a solution,
a t least one o ther answer
choice w o u ld also be a
solution. So, eliminate
9 and 10 as possible
answers. Guess th a t either
8 or 11 is correct and
check your guess.

Using the Distributive Property

Multiple Choice Which is a solution of 3(f + 1) - 4f & - 5?

CK)8 CE?9 CO 10 con

3(t+l)-4f>-5

Distributive Property

Combine like terms.

S ubtract 3 fro m each side.

Simplify.

Divide each side by -1. Reverse the inequality symbol.

8 Simplify.

8 is a solution of th e inequality 8. The correct answ er is A.

<£ G o t It? 3. W hat are th e solutions of 15 ^ 5 — 2(4m + 7)? C heck your solutions.

3f+3-4f> -5

-t+ 3 > - 5

-f+ 3-3 > -5 -3

-t> - 8

-t -8

-1 - -1

Why subtract 3n

instead o f 6n from

each side of the

inequality?

You can s u b tra ct e ith e r

3 n or 6 n fro m each side.

However, subtracting

3n gives you a variable

te rm w ith a p o sitive

coefficient.

Some inequalities have variables on b o th sides of th e inequality symbol. You n e e d to

gather th e variable term s on one side of th e inequality an d th e co n stan t term s on the

o th er side.

Solving an Inequality W ith Variables on Both Sides

What are the solutions of 6 n — 1 > 3n + 8?

6n - 1 > 3n + 8

6 n - 1 — 3n > 3n + 8 - 3n To g a th e r variables on th e left, s u b tra c t 3n fro m each side.

Simplify.

To g a th e r the con sta nts on the rig ht, add 1 to each side.

Simplify.

D ivide each side by 3.

Simplify.

3n - 1 > 8

3n - 1 + 1 > 8 + 1

3n > 9

3n ^ 9

3 3

n > 3

4 G o t It? 4. a. W hat are th e solutions of 3b + 12 > 27 - 2bl Check your solutions.

b. Reasoning The first step in solving Problem 4 was to subtract 3n from

each side of th e inequality. W hat else could have b ee n th e first step in

solving the inequality? Explain.

188 Chapter 3 Solving Inequalities