Page 899 - Algebra 1

Properties and Formulas
Properties
Addition Property of Equality
(19)
For every real number a, b, and c, if a = b, then a + c = b + c.
Addition Property of Inequality
(66)
For every real number a, b, and c, if a < b, then a + c < b + c.
Distributive Property
(15)
For all real numbers a, b, and c, a(b+c)=ab+acand(b + c)a = ab + ac. a(b-c)=ab-acand(b - c)a = ab - ac.
Discriminant
(113)
The discriminant of a quadratic equation ax2+bx+c=0,isb2 -4ac.
If b2 - 4ac > 0, there are two real solutions. If b2 - 4ac = 0, there is one real solution.
If b2 - 4ac < 0, there are no real solutions.
Division Property of Equality
(21)
For every real number a, b, and c, where c ≠ 0, if a = b, then _a = _b.
Also holds true for >, ≤, ≥, and ≠. Associative Property of Addition
(12)
For every real number a, b, and c, (a + b) + c = a + (b + c).
Associative Property of Multiplication
(12)
For every real number a, b, and c, (a ·b) ·c = a ·(b·c).
Commutative Property of Addition
(12)
cc
Division Property of Inequality
(70)
For every real number a, b, and c, where c > 0, if a < b, then _a < _b.
cc
For every real number a, b, and c, where c < 0, if
For every real number a and b, a + b = Commutative Property of Multiplication
(12)
For every real number a and b, a · b = b · a. Converse of Pythagorean Theorem
(85)
a < b, then _a > _b. cc
Also holds true for >, ≤, ≥, and ≠. Identity Property of Addition
(12)
For every real number a, a + 0 = a. Identity Property of Multiplication
(12)
For every real number a, 1 · a = a. Inverse Property of Addition
(6)
For every real number a, a + (-a) = 0.
b +
a.
If a triangle has side lengths a, b, and c, and
a2 + b2 = c2, then the triangle is a right triangle with a hypotenuse of length c.
Cross Products Property
(31)
For every real number a, b, c, and d, where b ≠ 0 and d ≠ 0, if _a = _c , then ad = bc.
bd
884 Saxon Algebra 1