Equation Examples Solving Linear Equations Subtract Divide

Equation Examples

Solving Linear Equations

subtract

divide by

Solving Linear Equations (including fractions)

(1/2)x = 4 + x multiply by (2/1) or

x = 8 + 2x

subtract

subtract x

-8 = x, or x = -8

Solving Inequalities

4x >

divide by

Intro to Functions

f (x) = 7x + 9

evaluate for x = 3

solve arithmetic f (3) = 30

Finding Slope

A line passes through (-5, 7) and (10, 17)

Find the rise (y2 -- y1)

Find the run (x2 -- x1)

Slope = rise/run

Finding the Equation of a Line

A line has a slope of -5/8 and a y intercept of (0, 3)

Standard linear equation from: y = mx + b, where m = slope and b = y at x = 0 (y intercept)

y = -(5/8)x + 3

Factoring Trinomials

Factor 3x2 + 4x --

The only way to create 3x2 is

(3x ) (x )

possibilities for -4 are

( -1) ( 4)

( 1) ( -4)

( -2) ( 2)

6x -- 2x = 4x, so (3x -- 2) (x + 2) = 3x2 + 4x --

Factoring Difference of Squares

Factor 32 -- 18x2

Factor out

2(16 -- 9x2)

Factor out square roots

2(4 -- 3x) (4 + 3x)

Factoring (Greatest common factor)

Factor 25x3y2 + 15x2y -- 10x2y3

Highest common factor for the coefficients is 5

5(5x3y2 + 3x2y -- 2x2y3)

Highest common factor for x is x2

5x2(5xy2 + 3y -- 2y3)

Highest common factor for y is y

5x2y (5xy + 3 -- 2y2)

Quadratic Formula

Solve 4x2 + 2x -- 3 = 0 using the quadratic formula.

Given ax2 + bx?

+ c = 0,

x = (-b +/- ((b2 -- 4ac))/2a

(-2 +/- ((22 -- 4(4)(-3)))/2(4)

(-2 +/- ((4 -- (-48))/8 = (-2 +/- (52/)8 = (-2 +/- 7.21)/8 = .651 or -1.15