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.