Download 2.1 Solving Linear Equations

Lesson 1a Notes Solving Multi-Step
Linear Equations
Definitions
Algebraic Expression –
mathematical expression involving
at least one unknown value
Algebraic Equation –
mathematical equation involving
at least one unknown value (a true
mathematical statement)
Definitions
Terms –
parts of the expression separated
by +/- signs
Like Terms –
terms which are “alike” (same
exponent on same variable) and
can be combined
+/-/×/÷ Properties of Equality
Adding, subtracting, multiplying or
dividing the same number to both sides
of the equation results in another
equivalent equation
Definitions
Solution –
a real number that can replace the
variable in an equation and make
the statement true
Examples
1. 4x + 8x = 17x – 9 – 1
2. 6 – (4 + m) = 8m – 2(3m + 5)
Conditional Equations
- A linear equation with one
solution
- When solved, x = a, where a is a
real number (zero included)
Identity vs. Contradiction
Identity Equation
• Infinite solutions,
solution set {all
real #’s}
• When solved,
final line is true, a
= a, where a is a
real number
Absurd Equation
• No solutions,
solution set Ø
• When solved,
final line is false,
a = b, where a
and b are real
numbers
Examples
1. 5(x + 2) – 2(x + 1) = 3x + 1
2. -4y + 3(y – 2) = -(y + 2)
Homework
p. 68
#12-36 ev, 65-74 all