linear equations and inequalities in one variable what is an equation? =
DESCRIPTION
Linear Equations and Inequalities in One Variable What is an equation?TRANSCRIPT
Linear Equations and Inequalities in One Variable
What is an equation?
=
Linear Equations and Inequalities in One Variable
What is an equation?
Linear Equations and Inequalities in One Variable
What is an equation?
Linear Equations and Inequalities in One Variable
What is an equation?
Properties of Equality
Reflexive Property
a = a
Properties of Equality
Symmetric Property
If a = b then b = a
Properties of Equality
Transitive Property
If a = b and b = c then a = c
Properties of Equality
Addition Property
If a = b then a + c = b + c
Properties of Equality
Subtraction Property
If a = b then a - c = b - c
Properties of Equality
Multiplication Property
If a = b then ac = bc
Properties of Equality
Division Property
If a = b and c = 0 then a/c = b/c
Properties of Equality
Whatever you do to
one side of an equation
Properties of Equality
do the same thing to the other side
Properties of Equality
and the two sides will stay equal
Examples
n – 6 = 9
Examples
n – 6 = 9Add 6 to both sides(addition property)
Examples
n – 6 = 9 +6 +6
Examples
n – 6 = 9 +6 +6 n = 3
Examples
n = 3
Examples
-35 = -5r
Examples
-35 = -5rDivide both sides by -5
(division property)
Examples
-35 = -5r -5 -5
Examples
7 = r
Examples
-3(m + 3) = 16
Examples
-3(m + 3) = 16
Distribute to get the m out of the parentheses
Examples
-3(m + 3) = 16-3m - 9 = 16
Distribute to get the m out of the parentheses
Examples
-3(m + 3) = 16-3m - 9 = 16
Add 9 to both sides(addition property)
Examples
-3(m + 3) = 16-3m - 9 = 16
+9 +9
Examples
-3(m + 3) = 16-3m - 9 = 16
+9 +9 -3m = 25
Examples
-3(m + 3) = 16-3m - 9 = 16
+9 +9 -3m = 25
Divide both sides by -3(division property)
Examples
-3m = 25 -3 -3
Examples
m = -25 3
Examples
4s + 6s = 100
Examples
4s + 6s = 100
Combine like terms
Examples
4s + 6s = 10010s = 100
Combine like terms
Examples
4s + 6s = 10010s = 100
Divide each side by 10(division property)
Examples
4s + 6s = 10010s = 100
10 10
Examples
s = 10
Examples
12 + 2g = 4 + 6g
Examples
12 + 2g = 4 + 6gMove the variable to one
side of the equation
Examples
12 + 2g = 4 + 6g -2g -2g
(subtraction property)
Examples
12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g
Examples
12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4gSubtract 4 from both sides
(subtraction property)
Examples
12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g -4 -4 8 = 4g
Examples
12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g -4 -4 8 = 4g
Divide both sides by 4
Examples
12 + 2g = 4 + 6g -2g -2g 12 = 4 + 4g -4 -4 8 = 4g 4 4
Examples
2 = g
Today’s Work:
Page 45Problems 7-20
When you finish, you may work quietly on any homework you have.