1 Expand 3x25x3 2 Solve for x 2x33xSolution1 3x 25x 3 3x5x

1. Expand. (3x-2)(5x+3)

2. Solve for x. |2x-3|=|3x|

Solution

1. (3x -2)(5x + 3) = 3x(5x+3) -2(5x+3) = 3x*5x + 3*3x - 2*5x -2*3 = 15x² +9x -10x -6 = 15x² - x - 6

2. I 2x -3 I = I 3x I . Therefore, (2x -3)² = (3x)² or, 4x² -12x + 9 = 9x² or, 9x² - 4x² + 12x - 9 = 0 or, 5x² + 12x - 9 = 0. Now, on using the quadratic formula, we have x = [ -12 ± { ( 12)² - 4*5* (-9)]/2*5 or, x = [ -12 ± ( 144 + 180)]/ 10 or, x = [-12±324]/10 or, x =(-12± 18)/10.Thus,either x =( -12 + 18)/10 = 6/10 = 3/5 or, x = ( -12-18)/10 = - 30/10 = - 3.