Download 2-3 Solving Equations Using Multipication and Division

Two operations that undo each other, such as addition and
subtraction, are called inverse operations. Inverse
operations help you to isolate the variable on one side of the
equal sign.
x  12  40
The problem.
Use inverse property.  12  12
x  28
Simplify.
x  15  32
 15  15
Check
x  15  32
?
  15  32

32  32

x  12  40
  12 ? 40

40  40
x  47

Formally check even numbered homework problems.
2-3 Solving Equations Using
Multiplication and Division
Algebra 1
Glencoe McGraw-Hill
Linda Stamper
What equation is shown on the scale?
To isolate the
variable, divide by
2, but to keep the
equation in balance
whatever you do to
one side you must
do to the other
side.
2x  6
1
2x  6
2 2
x 3
The value or values of the variable that make the
statement true is the solution to the equation.
Write an equation for the following:
There is only part of
a variable. To get a
whole variable use
repeated addition
1
which is known as x
4
multiplication.
x
 2
4
1
x
 4  4  2 4 
x 8
The value or values of the variable that make the
statement true is the solution to the equation.
Multiplication and division are inverse operations. You can
use multiplication to undo division, and division to undo
multiplication.
y
9
3x  15
Write the problem.
4
1
1
y
Use inverse property. 3x  15

4

 9 4 
3
3
Simplify.
4
x  5
y  36
Check
3x
3 
 15
 15
Check
y
9
4
 ? be in
The 4 must
9
the4numerator
position ormidway.
9  not
9 be
It should
written in the
denominator
position!
Example 1
m
 18
1 7
7   m  18 7 
7
 1  m  126  1
m  126
 18
Do your
 7 arithmetic
The 7 must be in
Solve.
Example 2
 4x  22
1
 4x  22
4
4
22
x
4
11
x
2
Example 3
 2 1 x  1


2
 4
1
2
1 4
4 9
  x  
2 9
9 4
4
x
18
2
x
9
calculations
off
the numerator
to or
the
side
position
midway.
Leave
the
fraction improper – in lowest terms.
(margins).
It should
not be
written in the
Usedenominator
good form - place the negative sign out front
in your
answer.
position!
Write an equation and then solve.
Ex.4 15 is the quotient of a number and negative 8.
=
n
15 
8 1
Do NOT switch the
n
 8 15   8

variable
to the other
 8 side of the equal sign
 120  n
unless you have reason
to move it!
CHANGING DECIMALS TO INTEGERS
You can multiply an equation with decimal coefficients by a
power of ten to get an equivalent equation with integer
coefficients.
Multiply each side of the equation by a power of 10 to
rewrite the equation without decimals.
Use the LCM (least common multiple) to determine the
power of ten needed to clear the decimal/s.
Recall that multiplying a number by 10, 100, or 1000 is
equivalent to “moving” the decimal point to the right one,
two, or three place respectively.
0.25 • 10 = 2.5
0.25 • 100 = 25
0.25 • 1000 = 250
Solve.
Write the problem.
Multiply by LCM.
Distribute.
Use inverse operations.
0.07m  0.21
1000.07m  0.21100
7m  21
7
7
m3
Solve.
0.035m  9.95  12.75
Write the problem.
10000.035m  9.95  12.75 1000
Multiply by LCM.
Distribute.
Use inverse operations.
Show division
work
neatly In
Remember:
beside
the work
algebra
downward. Line up
equation.
the equal signs.
35 2800
Skip
one line after
the answer.
35m  9950  12750
 9950  9950
35m  2800
35
35
m  80
Example 5 Solve. Round
to the nearest tenth.
4.6x  40.6  0.8
Example 6 Solve. Round
to the nearest hundredth.
3.35x  2.29  8.61
Example 7 Solve. Round to the nearest tenth if necessary.
0.007  0.7 x  0.21
You need to divide
to what decimal
position in order to
round to tenths?
You need to divide
to what decimal
position in order to
round to
hundredths?
Example 5 Solve. Round
to the nearest tenth.
Example 6 Solve. Round
to the nearest hundredth.
4.6x  40.6  0.8
3.35x  2.29  8.61
10 4.6x  40.6  0.8 10 1003.35x  2.29  8.61100
46x  406  8
335x  229  861
 406  406
 229  229
46x  414
335x  632
46
46
335 335
x9
x  1.886...
x  1.89
Example 7 Solve. Round to the nearest tenth if necessary.
0.007  0.7 x  0.21
10000.007   0.7 x  0.211000
7  700x  210
 210
 210
217  700x
700 700
0.31  x
0.3  x
2-A5 Pages 88-89 #14-25,28,46,55,57.