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
Solving Rational Equations
Solve ae + 9/(x -- 7) = 5/6
Multiply all numerators by (4)(x -- 7)
3x -- 21 + 36 = (20 + 5x -- 35)/6
Simplify
3x + 15 = (5/6)x -- (5/2)
subtract 15 and (5/6)x from both sides
(13/6)x = -(35/2)
multiply both sides by (6/13)
x = -(210/26) = -(105/13)
Fraction Exponents
Solve 275/3
Denominator of the exponent becomes the power of the radical
3(27
Numerator of the exponent becomes exponent of the radical term
(3(27)5
Simplify and solve
95 = 59,049
Solving Radical Equations
Solve ((x + 3) + 12 = 15
Subtract 12
((x + 3) = 3
square both sides x + 3 = 9
solve x = 6
