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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
Governments of Eastern Hemisphere nations Families, clan and tribal groups act to maintain law and order As settlement patterns changed, new political developed to meet the complex needs of society. Through time, the people have held different assumptions as to power, authority, governments and law. Governments change over time to meet changing needs and wants of the people Present systems of government have their origins in the past The value of the nations affect the guarantee
6. The rabbits will never die. The question was how many male/female rabbit pairs will be there after a year or 12 months? When the experiment begun, there is a single pair of rabbits. After duration of one month, the two rabbits have mated though they have not given birth. As a result; there is still only a single pair of rabbits. After duration of two months, the initial pair of rabbits will give
6 (18 - x) = 9 First, using the distributed property, we get: 3x + 10.8 -.6x = 9 Combining like terms we obtain: 3x + 10.8 = 9 Subtracting 10.8 from each side, we have: 3x = -1.8 Dividing both sides by -.3 we now solve for x: Now that x is known, we can plug this value into any of the original equations and obtain a value for y: y = 18 Returning to our original work problem,
Managerial Math Solve each of the following equations for the unknown variable. a) 15x + 40 = 8x - 15x +49 = 8x 49= -7x b) 7y - 1 = 23-5y Y= c) 9(2x + 8) = 20 - (x + 5) = 15-x d) 4(3y - 1) - 6 = 5(y + 2) Y = (20/7) Bob Brown bought two plots of land for a total of $110,000. On the first plot, he made a profit of 16%. On the
(Wolverine Tube Heat Transfer Data Book, 2009) Basic components of Shell and Tube Heat Exchangers include the following basic components although there is a plethora of existing specific features used in design of the Shell and Heat Tube Exchanger. The components specifically are: (1) Tubes -- "...the basic component of the shell and tube exchanger, providing the heat transfer surface between one fluid flowing inside the tube and the other fluid