2.
b)
Explain why 3x - 2 - 10 and 3x: 8 are not equivalent.
They do not haoe the same solution.
Given an equation, the properties of equality enable you to obtain an equivalent equation with
the same solution.
'l
.
Justif,i, using the properties of equahty, the following steps for isolating the unknown on one
side of the equality.
@
fhe-
umffi)@
\:ry!4,'
2.
3x-6:9
I
:15
3,t
You add 6 to each side
You diuide each side by 3
J
-q
Veriflr that "5" is the solution to each of the preceding equations.
... .
.
SO1UING AN EOUATION
.
To solve an equation, use the properties of equality in order to isolate the unknown on one
side of the_equality.
Ex.: 3x-2:10
3x-21-7:10 I2
3x: 12
x: 4
Verify: 3x4-2:lA
Add2toeachside
Reduce
Divide each side by
3
The solution to the equation is 4. Write S : {4}.
5x +
i0 + 3r.
5x -f 4 -- 3.r: l0 + 3x* 3x Subtract 3x from each side
2x I 4: l0
Reduce
2x + 4 *^4:
Subtract4 from each side
-4
Ex.:
4:
i0
'oL-J
Verify: 5x3-l=2
4:19
10+3x3:19
L;f,:'"""".h
side bv
)L 2
The solution to the equation is 3. Thus S : t3).
€.
Solve the following equations.
*) 5x-3:12
c) 72:4-2x
*) 3x* 1:5
s=lsl
b)
s={-a}
d)
s={tl
f)
-1
s
s=r*,
hi
l.5x-0.2:0.8
J
fil'x-1:'
r'24
m*
-2x-t 3: -15 :3x
5
*3
3-/
2
s
={41
s = t-6t
s={4}
-/--1
s={31
Solve the following equations.
a) 2x -13 :3x - 4
c} (x-rl+2(x- 3) :x*5
C Gucrin. editeur lt€e
s=t7l
s=16l
b) 6x
d)
s=tsl
- 2:3x -17
3(4x+1):2(3x-1)
s = t-Tt
7.1 Equations
75
s=lol f)
-2(3x
e) (2x- 1)-(3x+21 :4x-3
g) 5l2x + 1) - 3(2x- l) :
m.
2l3x
- zls:fl
h) 3
-
6(x
bi
2
+
5)
-
+
1)
(x
-
3)
:3(7x
- ll
S=IHI
+ 4(3x - 2) : 2x -t zs = tit
Solve the following equations.
3x_ 1_3^_
3".
1_ 3
II
a)
'2 :^-l---tt- 3 4
-!')?-x*l
x-l
s =t4t
9
S=[-51
^
d)
--x
3
2x -13
3
LJ
&.
s=F+1
13
44
s=tzt
3x-1
-
2
Solve the following equations.
-r'236x-l
x*l
x-l
'3226
s-
s=rf,
7
x Fl , 3
rl
bi x-2
s = {15}
I
d)
x*1
35
2x -11 3x J1 --:
s = {14}
1
1a
x-l _
43
x-11
s={+t
Solve the following equations.
a)
-5(2x
b)
')
a(x+1)1
+ 1)+
J
c)
3(x
- 2l: 2(4x -
){+" -
2x-3 -
z)
1l
-
: |ttzx + s)
-
3(2x
3)
s = {-2}
s=r*,
3
+^
s
=
{-*t
4
dl *-1, *-2:I
Jf
ar 2x-1 3xl-1_5
'326
&.
-
s=l2l
s
= {-21
The following equations either have a unique solution, infinite solutions or no solution. Solve
them.
a) 3(2x-t i)-(x -3) :6
c) 2(3x-l)-312x*1):-5
s=lo]
bi
S=R
ut
2(3x
+
rr 3x+1
'24
1)
:3(2x-
6x-3
1)
s=o
s=a
F.
Nancy is 2 years older than her brother Eric. In 5 years, the sum of their ages will be equal to
40 years. What is the present age of eachT
x: Eric's age; (x + 7) + (x + 5) = 4O; x = 14. Eric is 14 years old and Nancy is 76 years old.
€.
Today, Frank is 4 years older than Maria. Six years ago, Frank was twice as o1d as Maria. What is
Frank's present ageT
x: Maria's age; (x -2) = 2(x -6); x = 7O- Frank is 74 vears old.
t*
S_teve is 4 years older than Rose. In 5 years from now, the sum of their ages will be equal to twice
the sum of their ages from 5 years ago. What is Steve's present age?
x: Bose's age; (x + 9) + (x + 5) = 2 [(x - 7) + (x - 5)]; x = 73. Steue is 77 years old.
! ffi"
76
of 30 students, there are 6 more girls than boys. How many girls are there in the class?
x: number of boys; x + (x + 6) = 3O; x = 72. There are 78 girls in the class.
L-t a class
Chspter 3
Equations and inequatities
O Guerin, 6diteur ltee