Two operations that undo each other, such as addition and subtraction, are called inverse...
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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.
Check
The problem.
4012x Use inverse property.
12 1228x Simplify.
4012x 4012
4040
3215x 15 15
47x
3215x 3215
3232
28 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? 6 x2 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.
2 2x 3
The value or values of the variable that make the statement true is the solutionsolution to the equation.
1
6 x2
Write an equation for the following:
2 4x
There is only part of a variable. To get a whole variable use repeated addition which is known as multiplication.
4 4
x 8
The value or values of the variable that make the statement true is the solutionsolution to the equation.
x41
1
2 4x
15x3
94y
4 3 15x3
Multiplication and division are inverse operations. You can use multiplication to undo division, and division to undo multiplication.
Check
1
Check
3 5x
15x3
3
15
4
36y
94y
9
4
99
Write the problem.Use inverse property.Simplify.
?
5 36
The 4 must be in the numerator
position or midway. It
should not be written in the denominator
position!
94y
1
15
The 7 must be in the numerator
position or midway. It
should not be written in the denominator
position!
Example 1
1
187m 7 7
Do your arithmetic
calculations off to the
side (margins).
7 18
126m
187m
Solve.
Example 2
122 x4
4 4
422
x
Leave the fraction improper – in lowest terms.
211
x
Use good form - place the negative sign out front in your answer.
22 x4 Example 3
1
21
x49
94
94
184
x
92
x
21
x41
2
2
1 1
126m
Write an equation and then solve.
Do NOT switch the variable to the
other side of the equal sign unless
you have reason to move it!
Ex.4 15 is the quotient of a number and negative 8.
1
8n
15 8 8
n120
=8
n15
CHANGING DECIMALS TO INTEGERSYou can multiply an equation with decimal coefficients
by a power of ten to get an equivalent equation with integer coefficients.
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
Multiply each side of the equation by a power of 10 to rewrite the equation without decimals.
Solve.
Write the problem.
21.0m07.0
Multiply by LCM. 21.0m07.0 21m7
7 7 Use inverse operations. 3m
100
Distribute.
100
Write the problem.
75.1295.9m035.0
Multiply by LCM. 75.1295.9m035.0
12750 9950m35
Use inverse operations. 9950 99502800m35
53 53 80m
Show division work neatly beside the equation.
280035
Solve.
Distribute.
1000 1000
Remember: In algebra work
downward. Line up the equal
signs. Skip one line after the
answer.
Example 5 Solve. Round to the nearest tenth. 8.06.40x6.4
You need to divide to what
decimal position in order to round
to tenths?
Example 6 Solve. Round to the nearest hundredth. 61.829.2x35.3
You need to divide to what
decimal position in order to round to hundredths?
Example 7 Solve. Round to the nearest tenth if necessary.
21.0x7.0007.0
Example 5 Solve. Round to the nearest tenth. 8.06.40x6.4
8.06.40x6.4 8406x46
406 406414x46
46 46 9x
10 10
Example 6 Solve. Round to the nearest hundredth. 61.829.2x35.3
10061.829.2x35.3100 861229x335
229 229632x335
335 335 ...886.1x
89.1x
Example 7 Solve. Round to the nearest tenth if necessary.
21.0x7.0007.0
100021.0x7.0007.01000 210x7007
210 210x700217
007 007 x31.0 x3.0
2-A5 Pages 88-89 #14-25,28,46,55,57.