Algebra I Review, part 1

Homework:

Create and solve 5 single-step and 3 two-step linear equations to be turned in. Don't forget the heading!

Notes:

Basic Rules of Algebra:

Commutative: a + b = b + a; ab = ba
Associative: (a + b) + c = a + (b + c); (ab)c = a(bc)
Distributive: a(b +c) = ab + ac; a(b – c) = ab – ac
Identity: a + 0 = a; a ∙ 1 = a
Inverse: a + (-a) = 0; a ∙ 1/a = 1
Multiplication:
(-1)a = -a
(-1)(-a) = a
a ∙ 0 = 0
(-a)(b) = -ab
(-a)(-b) = ab

Equations of Lines:

Slope-intercept form: y = mx + b
General form: Ax + By + C = 0
Point-slope form: y – y1 = m(x – x1) [(x1,y1) point on line]
Horizontal line: y = b
Vertical line: x = a

Distance formula: √(x2 – x1) + (y2 – y1)
Midpoint formula: x1 + x2 , y1 + y2
2 2

Problem Solving:

1. Understand the problem. Read the problem carefully. Decide what information you are given and what information you need to find. Eliminate unnecessary information.
2. Make a plan to solve the problem. Choose a strategy. PEMA. Equation/formula. Look for a pattern. Break into simpler parts. Work backwards. Make a table.
3. Carry out the plan to solve the problem.
4. Check to see if your answer in reasonable.

Solving Linear Equations

1. Get x by itself.

x+12=25 x-6=0 -36/-9=-9x/-9

-12 -12 +6 +6 x=4

x=13 x=6

-32x/-32=4/-32 -6=x+4 3x-4=20

x=-0.125 -4 -4 +4 +4

-10=x 3x/3 24/3

x=8