1-5 Skills Practice

,~ .j Solving InequalitiesSolve each inequality. Describe the solution set using set-builder or intervalnotation. Then, graph the solution set on a number line.1.5_>2 (z _7--< -8} O~-i-co~ --:3]

2.3a + 7_< 16

-9-8-7-6-5-4-3-2-1

3. 16<3q +4 {qiq>-~ ,-~}

-4-3-2-101234

-101234567

5. 3x ~ -9 {;;1 ;f ~ --3} 0:" [--37 ~}

-4-3-2-101234

-4-3-2-10 1 2 3 4

7. 2z < -9 + 5z ,Zt Z >o~-~ O~" !{3, co}

-2-10 1 2 3 4 5 6

9. -3s -

-4-3-2-10 1 2 3 4

11. 0.7m + 0.3m --> 2m - 4 ~ml m _< 4}or (-co, 4]

-2-10 1 2 3 4 5 6

13. 1.7y - 0.78 > 5 {Yl Y > 3.4}

or (3.4, ~)

-2-10 1 2 3 4 5 6

¯ I I I I t I 1:-I--1 --4-3-2-10 1 2 3 4

-4-3-2-1 0 1 2 3 4

’-[--4 -31-21 I ’0;~13~’-1 (--co,- ~---" l!

14.@- 9>2z + 1 {X IX> 5} or (5, co}

-101234567

Define a variable and write an inequality for each problem. Then solve.

15. Nineteen more than a number is less than 42. ~ ÷ ~ ~ ( 42; ~ ~ 23

16. The difference of three times a number and 16 is at least 8. $~ - ~ fi ----- ~; ~ >-- ~

17. One half of a number is more than 6 less than the same number. ~ ~ ~ ~ - ~; ~ ~ ~ 2

18. Five less than the product of 6 and a number is no more than twice that same number.

~n - 5 -< 2n; n-< ~

© Glencoe/McGraw-Hill 27 Glencoe Algebra 2

2:<:<,%~ ~ N A M E D AT E P E RIO D~i~:~::., ~ .......

1-5: Practice (Average)

Solve each inequality. Describe the solution set using set-b~lder or inte~alnotation. Then, ~aph the solution set on a n~ber line.

1. 8x - 6 ~ 10 {X~ X ~ 2} 0~" [2~ =} 2. 23 - 4u < 11 {~’~ 5 > 3} 0~" (~ =}

¯ I I ~ ~ I I ~ ~1~ ’ I I I ~ I I I I 1’-4-3-2-1 0 1 2 3 4 -2-1 0 1 2 3 4 5 6

g. 9x- 11>6x-9 x~X> Or ,~ &-a(4w- 1)>18 w~w< 4~

-4-3-2-1 0 1 2 3 4 -4-3-2-1 0 1 2 3 4

9.9(2r-5)-3<7r-4{r[¢< 4} 10.1 +5(x-8)~2-(x+5){Z[Z~ 6}

:r I--:-l---r--’,---’, ’, ’, ~ or(-~,4} -I-If-!--t-t !t I. or(-~,~-2-1 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8

¯ I t I ~ I 1 I 1 1 * ~-’,-I-I I---~ -I I I I :-4 3 2 1 ~ 1 2 3 4 -4 3 2 1 ~ 1 2 ~ ~

13. -36 - 2(w + 77) > -4(2w + 52)

-4 -3-2 -1 0 1 2 3

14.4n- 5(n- 3)>3(n + 1)-4{nl ,’~ < 4} Or (--co, 4)~-I-~ I-I---[--’,--q- -1 ’, ’, :

-2-1 0 1 2 3 4 5 6

Define a variable and write an inequality for each problem. Then solve.

15. Twenty less than a number is more than twice the same number.n-20>2n;n<-20

16.Four times the sum of twice a number and -3 is less than 5.5 times that same number.412n + (-3)] < 5.5n; n < 4.8

17. HOTELS The Lincoln’s hotel room costs $90 a night. An additional 10% tax is added.Hotel parking is $12 per day. The Lincoln’s expect to spend $30 in tips during their stay.Solve the inequality 90x + 90(0.1)x + 12x + 30 -< 600 to find how many nights theLincoln’s can stay at the hotel without exceeding total hotel costs of $600. 5

18. BANKING Jan’s account balance is $3800. Of this, $750 is for rent. Jan wants to keep abalance of at least $500. Write and solve an inequality describing how much she canwithdraw and still meet these conditions. 3800 -- 750 -- ~.f >-- 500~ W ~< $2550

© Glencoe/McGraw-Hill 28 Glencoe Algebra 2