DATE
NAME
P E R IOD
elvention
Solving Equationsby Multiplying or Dividing
Solve Equations by Dividing Just asadditionandsubtraction
areinverseoperations,
multiplication and division are inverse operations. To isolate a variable in an equation
involving multiplication, you can apply the Division Property of Equality.
Division
Property
of Equality
If you divide each side of an equation by the same nonzero number, the two
sides remain equal.
Solve -7x = 42. Check your solution and graph it on a number line.
-7x =
-7x =
- -7
lx=
x :
CHECK:
42
42
--7
-G
Writethe equation.
-G
ldentityPropefi; 1x : x
-7x = 42
L 42
-7(-6)
42 = 42 r'
DivisionPropertyof Equality
-7 + -7 = 1 ,4 2+ -7= -6
write the equation.
Replace
x with -6 andcheckto seeif the sentence
is true.
The sentenceis true.
-6
The solution is -6.
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
0
To graph -6, draw a dot at -6 on the number line.
o
c
o
o
E
(U
o-
E
o
o
I
=
()
I
Exercises
Solve each equation. Check your solution.
1. - Ba :
15
2. - t:
3. 7r :28
5
E
(5
o
-c
F
o
o
(t)
4. 2 4 : -8m
5. -LLb - 44
6. Lzd: - 48
7. -10p - 10
8 . -1 L w - -3 3
9. L2S: 42
E
(6
I
=
g
(,o
I
b
o
o
c
o
o
o
(')
10. -LIr:
IzL
11 . 6 d :
L26
L2. Lzb: 108
oo
o
13. 0.4m: 20.4
Chapter4
L4. -0.7y - 8.4
23
15. 0.9t - 0.63
Glencoe Pre-Algebra
f-
DATE
NAME
lili[ivention
P E R IOD
kontinued.)
SolvingEquationsby Multiplyingor Dividing
Solve Equations by Multiplying
\**
to isolatea variablein an equationin whicha
variable is divided, you can apply the Multiplication Property of Equality.
Multiplication Property of Equality
If you multiply eachside of an equationby the samenumber, the two sidesremain equal.
's;il;
t:--z.check
your solution.
Writethe equation.
MultiplicationPropeftyof Equality
InversePropertY;2.
Multiplicative
I:
I
ldentityProperty.Check your solution.
g6b"fib.checkyoursolution.
ffif
2 b : tS
writetheequation.
b
-g (-*),
= -f
[b :
-18
b = -18
(EJ
-f.
sideor -3,whichisthereciprocaror
Muftipry
each
Inversepropefi'-8 (-*) = t
Muttipticative
ldentityPropefi.Checkyoursolution'
Exercises
o
o
E
Solve each equation. Check your solution.
.t
(o
=
n
1. -1 4
'+
@
o
o
f
o
o
o
\o
4.
T=: -1
-D
o
il
€
-
b. +b - 2 2
I
A)
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o
:t
o
<r
7'# - -L4
8.+-
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{=
e.$;:18
o
c)
o
s€
I
T
o
o
3
10.
]S
- B0
1 3f.t n :7 2
Chapter4
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q)
=
q --4
L 2 . _ID
1 1.Lr U: 49
o
v,
5
o
1 5 .ff:6 4
L 4 .# _ 2 5
24
t"*
Glencoe Pre-Algebra