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Unformatted text preview: g Activity — Solving inequalities Solve these inequalities for real numbers. 1 1—x_6
2 lbw2:5
3 4<3{Zbl)
4 4552
3
5 3{12a):?
6 2d+35_4
5
2.: x l
T T725 3 2{4+ a): 3(23a) AGtiVity — Solving inequalities l 3hI5
Stu5 diﬁde both sick3 by l
5 .. .
IiiE :1de both sides by}
. . 5
Solution is all malmmept for E
2 3:be
.,,1
y 3
3 4:6113
Ebb3:4 readmgﬂumrighttoleﬁ
65>?
Ina1  g s 2 subtract 4 ﬁcrn each side x z 6 multiply each side by  3 {sign changes) 36a'a'?
6a e 4 subtract 3 here each side
4 . . . .
a e E dmde heth atdes by 6 {change algn)
2
a:—
3
2d+352ﬂ multiply bDﬂl sides byﬁ
2d523
iiiE er «Q'sl2l
2 2
5x 1 , . .
£22 wnte LHSasastngle frachen
sz Drxzé 01‘le.2 01‘ 5:211
III} 5 5
3+2acﬁ9a 11a 1:: 6  3 add 9a to each side, euhhact 3 frem each side
11:: u: 2 2 . . .
a «r. H dlwde bcﬂl sldes by 11 g Activity — Solving problems involving inequalities Solve these problems by ﬁrst forming an inequality. Draw a number line
sketeh for eaeh. 1 Three less than four times a number is not equal to 5. What integer
values can the number take? 2 When the produet of 6 and a number is subtracted from 2, the result
is not more than 11}. a What values ean the number take if it is real?
b What is the ﬁrst integer value the number can take? 3 The reciprocal of a number is greater than 2. a What real values ean the number take?
b Is zero a possible solution? Why? 4 Five more than three times a number is not less than the sum of
seven and twiee the number. a What is the ﬁrst integer value the number ean take? b What real values satisfy this statement? Activity — Solving problems involving in equeliti ee Eaeh problem should start with the line ‘let the number he x‘ although
you ean uee any pronumal you like.
1 4a:  3 F 5
x a 2
Sinee x is an integer, x  ... 2,l,t},l,3,4,... {all integers exoept 2) 4—i—ﬁ—ﬁ—i—l—i—ﬁ—i—
—3—2 —1{] 1 2 3 4 5 2 26:;5 It} 1not more than‘ means‘lese than erequal to‘
6x 5 3
4
(I x2—
{ i 3
{In} xl
—l—l—I—l—l—l—l—II
—3 —2 ‘3—1 [1 1 2
3 132 {It} Ne, sinee e is not less than _ l 2
3x+52T+2x
—i—i—¢—i—i—i—r
“”2 o 1 2 a 4
{a} xZ (b) all real values of x which are 2 2 Solve those equations using tho subatituﬁc
1 x‘  3x2  4  o 2 y‘+4y=+3o
3 ﬂsﬁsao 4 {d+ If ’l{d+1)+1o o 5 2{m+3)‘3{m+3)22ﬂ Activity — Solving equations using a oh anga of variable 1 x‘3x24Il} 1123114{1 pintoJr;2
[u4)[u+1)o faotoriso
114 01‘ ul 2 1524 or x l roplaooubyxz Thoro 31o only 2 solutions: x  :2 2 y‘+4y*+3o
H2+4H+3lﬂ pintoy2
{n+3){u+1)o faotoﬁao
H3 or Hl y23 or y2l roplaoBHbny Thoro are no possible solutions. 3583641 xzSxBﬁﬂ' putt£2 {x _ 9){x+ 4)  n factorise
x9' or x4 129 or I24 mplaﬂﬁxb‘yti There are 2 possible wlutions: I  =3 {d+l)zT{d+l)+lt}t]
azTa+lt}{II putaa'+l {a 5){a2)ﬂ aS or aZ d+l5 0r d+l2 d4cr 41 Check solutions: whendrt LHssttxsnuu
whendl LHSZETx2+lt}t} 2[m+3.)‘3.[m+3.)2 2t}
ZkzﬁZt} put{m+3)zk
[2k+l){k2)t} l
k— or tic2
2 thus [m + 3f   l which has no solution or 2
{m+3)2 2 whichis .012 +6m+Tlﬂ
this equation can be: wlved using the quadratic for tagetm 452,5 or tau3:6 [ﬁg2J3 (a) Solve the following equation for x: Zak—ex: [L l Salve ﬂiese inequalities:
3.:  2
5 a 24 b 1521%: k+3 c 5(12x)<3x+l ...
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 Spring '10
 wilson
 Math, Inequalities

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