the multiplication principle of equality 2.3a 1.solve linear equations using the multiplication...
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The Multiplication Principle of Equality2.3a2.3a
1. Solve linear equations using the multiplication principle.
2. Solve linear equations using both the addition and the multiplication principles.
ReviewReview
45
54
1
1
1
1
111
Multiplicative Inverses(Reciprocals)
32
18
32
118
6
1
12112
32
186
1
12
Multiplication Principle of EqualityMultiplication Principle of Equality44
4242 88
33 3232
66
1010
1021
1021
55
1010
210
210
55
The Multiplication Principle of EqualityIf a = b, then ac = bc for all real numbers a, b, and c, where c 0.
Multiplying by ½ and dividing by 2 are equivalent!
Multiplication Principle of EqualityMultiplication Principle of Equality
Multiply both sides of the equation by the multiplicative inverse of the coefficient
or
Divide both sides by the coefficient.
168 x
1681
881 x
1
1
1
2
21 x2x
816
88 x168 x
1
1
1
2
21 x2x
If the coefficient is a fraction, multiply by the multiplicative inverse (reciprocal).
If the coefficient is an integer, divide.
Multiplication Principle of EqualityMultiplication Principle of Equality
157 x715
77 x
1
1
118y
1565 y
56
1565
56
y1
1
1
-3
1
1
18y
715x
Addition and Multiplication Principle of EqualityAddition and Multiplication Principle of Equality2374 x
To Solve Linear Equations1. Simplify both sides of the equation as needed. a. Distribute to clear parentheses. b. Combine like terms.2. Use the addition principle so that all variable terms
are on one side of the equation. 3. Use the addition principle so that all constants are
on the other side. 4. Use the multiplication principle to isolate the
variable.Use the addition principle BEFORE the multiplication principle!!!
Addition and Multiplication Principle of EqualityAddition and Multiplication Principle of Equality
2374 x 1. Simplify 2. Move the variable terms. 3. Move the constants.4. Isolate the variable.
77
164 x444x
Check:
23232371623744
Addition and Multiplication Principle of EqualityAddition and Multiplication Principle of Equality
72125 xx1. Simplify 2. Move the variable terms. 3. Move the constants.4. Isolate the variable.
7123 x1212
53 x33
35x Check:
777125
712315
7310
12325
735
21235
5
Addition and Multiplication Principle of EqualityAddition and Multiplication Principle of Equality
2925243 mm1. Simplify 2. Move the variable terms. 3. Move the constants.4. Isolate the variable.
Check:
29410123 mm2922 m2222
7m
Addition and Multiplication Principle of EqualityAddition and Multiplication Principle of Equality
93352 xx1. Simplify 2. Move the variable terms. 3. Move the constants.4. Isolate the variable.
Check:
933102 xx9372 xx
xx 33
165 x
77 975 x
55
516x
Addition and Multiplication Principle of EqualityAddition and Multiplication Principle of Equality
795172 mmm 1. Simplify 2. Move the variable terms. 3. Move the constants.4. Isolate the variable.
Check
795172 mmm78515 mm
mm 55
m38
77 7315 m
33
m38
38m
Addition and Multiplication Principle of EqualityAddition and Multiplication Principle of Equality
524543 xxxx1. Simplify 2. Move the variable terms. 3. Move the constants.4. Isolate the variable.
5242 xxxx 22
54
Contradiction
Solution: No solution or
Addition and Multiplication Principle of EqualityAddition and Multiplication Principle of Equality
523442 xxx 1. Simplify 2. Move the variable terms. 3. Move the constants.4. Isolate the variable.
8282 xxxx 22
88
Identity
Solution: All Real Numbers
Solve. 8m + 6 = 3(12 + 2m)
a) 3
b) 5
c) 8
d) 15
2.3
Solve. 8m + 6 = 3(12 + 2m)
a) 3
b) 5
c) 8
d) 15
2.3