Objective- To solve equations in the form ax + b = cx + d and inequalities in the form ax + b < cx + d Solve. 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

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

Problems Involving Inequalities Solve. -3( x - 5 ) + 7 < 4( 3x + 2) -3x + 15 + 7 < 12x + 8 -3x + 22 < 12x + 8 +3x +3x 22 < 15x + 8 - 8 - 8 14 < 15x 15 15 x > < x

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 maple be taller than the beech? 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