3-3 Solving Inequalities Using M ultiplication or Division
Quick Review
Y o u c a n u s e th e m u l t i p l ic a t i o n a n d d iv is io n p r o p e r t ie s o f
in e q u a lit y to t r a n s f o r m a n in e q u a lit y. W h e n y o u m u l t i p l y o r
d iv id e e a c h s id e o f a n i n e q u a l i t y b y a n e g a tiv e n u m b e r , y o u
h a v e t o re v e rs e th e i n e q u a lit y s y m b o l.Ex a m p l e
What are the solutions of — 3x > 12?
-3 x > 12
—3 x < 12^^ Divide each side by - 3. Reverse the
-3 -3 inequality symbol.
x<-4 Simplify.A
Ex e r c i s e s
Solve each inequality. Graph your solutions.- 5x < 15
- —6t > 18
- f < 2
- -|<6
- 25.5g> 102
- |n > -9
- 44.5 < 2.7d
- -17.1m < 23.8
- Part-Time Job You earn $7.25 per hour baby-sitting.
Write and solve an inequality to find how many full
h o u r s y o u m u s t w o r k to e a r n a t le a s t $ 2 0 0.
3-4 Solving M ulti-Step Inequalities
Quick Review Ex e r c i se s
W h e n y o u s o lv e in e q u a lit ie s , s o m e tim e s y o u n e e d to u s e
more than one step. You need to gather the variable termsSolve each inequality.o n o n e s id e o f th e i n e q u a lit y a n d th e c o n s t a n t t e r m s o n th e 29. 4k- 1 > -3
other side. 30. 6(c — 1) < -18- 3t>5t+ 12
Ex a m p l e
What are the solutions of 3x + 5 > - 1? - —|y - 6 > 42
3x + 5 > — 1 33. 4 + tt^2 > 2x
3x > - 6 Subtract 5 from each side. 34. 3x + 5 < 2x - 8
x > - 2 Divide each side by 3. 35. 13.5a+ 7.4 <85.7- 42w > 2{w + 7)
- Commission A s a le s p e rs o n e a rn s $ 2 0 0 p e r w e e k
p lu s a c o m m is s io n e q u a l t o 4% o f h e r sales. T h is
w e e k h e r g o a l is to e a r n n o le ss t h a n $ 4 5 0. W r it e a n d
s o lv e a n i n e q u a l i t y to f i n d th e a m o u n t o f sa le s s h e
m u s t h a v e t o r e a c h h e r g o a l.
2 2 4 C h a p te r 3 C h a p te r R eview