Thii^k
Is th e r e a n o th e r
way to solve this
inequality?
Yes. In s te a d o f u s in g th e
Distributive Property, you
can firs t divide each side
by 2.Without solving, how
can you te ll th a t this
inequality has no
solution?
The variable terms
on each side o f th e
inequality are equal, but- 5 is not g re a te r th a n 7.
S om etim es solving an inequality gives a statem en t th a t is always true, such as 4 > 1. In
th a t case, the solutions are all real num bers. If th e statem en t is never true, as is 9 < - 5 ,
th e n th e inequality h as no solution.In eq u alities W ith Special Solutions
0 W h a t are the solutions of 10 — 8a a 2(5 — 4a)?
10 - 8a > 2(5 - 4a)
10 - 8 a > 10 — 8 a Distributive Property
10 - 8 a + 8 a > 10 - 8 a + 8 a Add 8 a to each side.
10 > 10 Simplify.
Since th e inequality 10 > 10 is always true, th e solutions of 10 - 8 a ^ 2(5 - 4a) are
all real num bers.0 What are the solutions of 6m — 5 > 7m + 7 — m?
6 m — 5 > 7m + 7 — m
6 m — 5 > 6 m + 7 Simplify.
6m - 5 - 6 m > 6 m + 7 - 6 m Subtract 6 m fro m each side.
-5 >7 Simplify.Since th e inequality - 5 > 7 is never true, th e inequality 6 m — 5 > 7m + 7 — m has
no solution.G o t It? 5. W hat are th e solutions of each inequality?
a. 9 + 5n ^ 5n — 1 b.^8 +^6 x ^ 7x + 2 — xJ Lesso n Ch eck^
Do y o u k n o w H OW?
Solve each inequality, if possible. If the inequality has
no solution, write no sol ut i on. If the solutions are all
real numbers, write al l real numbers.- 7 + 6 a > 19
- 2(f + 2) - 3 f > —1
- 6 z — 15 < 4z + 11
- 18x - 5 < 3(6x - 2)
- The p erim eter of a rectangle is at m ost 24 cm. Two
opposite sides are b o th 4 cm long. W hat are th e
possible lengths of th e o th er two sides?
MATHEMATICAL
Do y o u UN DERSTAND? 1 0 9 PRA CTICES
6. Reasoning How can you tell th at th e inequality
3 1+ 1 ^ 3/ f- 2 has no solution ju st by looking at
the term s in th e inequality?- Reasoning Can you solve the inequality
2(x - 3) < 10 without using th e D istributive
Property? Explain. - Er r o r A n a l y s i s Your friend says that the solutions
of th e inequality - 2 ( 3 - x) > 2x - 6 are all real
num bers. Do you agree w ith your friend? Explain.
W hat if th e inequality sym bol w ere >?
c
Po w erAlg eb ra.com. —.i...
j Lesso n 3- 4 So lving M ult i- St ep In eq u alit ies^189