Math 101

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Mathematics for Management Concept Summary
Algebra
Solving Linear Equations in One Variable
Manipulate the equation using Rule 1 so that all the terms involving the variable (call it x) are on one side of the equation and all constants are on the other side. Then use Rule 2 to solve for x.
Rule 1: Adding the same quantity to both sides of an equation does not change the set of solutions to that equation.
Rule 2: Multiplying or dividing both sides of an equation by the same nonzero number does not change the set of solutions to that equation.

Straight Lines: Slope Intercept Form
A straight line with slope m and y-intercept (b, 0) has the equation y = mx + b.

Point Slope Form of a Line Equation −

Given two points on a line, (x0, y0) and (x1, y1), find the line's slope m = 1 −0 .
1

0

Then the equation of the line may be written as y – y0 = m(x – x0).

Solving Two Linear Equations
Two linear equations in two variables (call them x and y) have no solution, an infinite number of solutions, or a unique solution. You may solve two linear equations by either substitution or elimination.


Substitution: Use one equation to solve for one variable in terms of the other (say, x in terms of y). Then substitute this relationship for each occurrence of x in the remaining equation. Now solve the remaining equation for y. Given that you know x in terms of y, you also know x.



Elimination: Add a multiple of one equation to the other equation to eliminate a variable (say, x) from the other equation. Solve the resulting equation for the remaining variable (y). Substitute this value of y in either of the original equations to find x.

Linear Inequalities: One Variable
Use the following rules to solve for the set of values satisfying a linear inequality.


If you add the same number to both sides of an inequality, the resulting…...

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