Steps for Solving Equations! Distribute Combine Like Terms on each side of = Move variables to one side of = and constants (numbers) to the other side Undo addition or subtraction Undo multiplication or division Simplify

Objective- To solve equations in the form ax + b = cx + d. 14k + 20 = 21k - 43 -14k -14k 20 = 7k - 43 + 43 + 43 63 = 7k 7 7 9 = k

Solve. x + 1.05x = 2x - 1000 2.05x = 2x - 1000 -2x -2x 0.05x = -1000 0.05 0.05 x = -20,000

Solve. - 2y + 11 = - 6y +2y +2y 11 = - 4y - 4 - 4 -2.75 = y

When do they cost the same? 250 + .01n = 70 + .03n - .01n - .01n An Easier Way of Doing Printing Problem! Let n = number copies Let C = total charge Acme Best C = 250 + .01n C = 70 + .03n When do they cost the same? 250 + .01n = 70 + .03n - .01n - .01n 250 = 70 + .02n They cost the same at 9000 copies. 180 = .02n .02 .02 9000 = n

Problem In 1990, the population of El Paso was 515,000 and increasing at 9000 people per year. Milwaukee was 628,000 and decreasing at 800 people per year. When will they be the same? Let n = number of years Let P = population El Paso Milwaukee P = 515,000 + 9000n P = 628,000 - 800n

Let n = number of years Let P = population El Paso Milwaukee P = 515,000 + 9000n P = 628,000 - 800n 515,000 + 9000n = 628,000 - 800n + 800n +800n 515,000 + 9800n = 628,000 -515,000 -515,000 9800n = 113,000 9800 9800 n 11.53 years

Tree Problem A beech tree is 8 ft. tall and grows ft. per year. A maple tree is 3 ft. tall and grows 1 foot per year. When will the trees be the same height? Let x = number of years Let h = height of tree Beech tree Maple tree h = 8 + 0.5x h = 3 + x

When is maple taller than beech? Let x = number of years Let h = height of tree Beech tree Maple tree h = 8 + 0.5x h = 3 + x 8 + 0.5x = 3 + x - 0.5x - 0.5x 8 = 3 + 0.5x 5 = 0.5x x = 10 years 10 = x