Solve for x:x/5 - 2 = x/2 + 3 Put each term in x/5 - 2 over the common denominator 5: x/5 - 2 = x/5 - (10)/5:x/5 - (10)/5 = x/2 + 3 x/5 - (10)/5 = (x - 10)/5:(x - 10)/5 = x/2 + 3 Put each term in x/2 + 3 over the common denominator 2: x/2 + 3 = x/2 + 6/2:(x - 10)/5 = x/2 + 6/2 x/2 + 6/2 = (x + 6)/2:(x - 10)/5 = (x + 6)/2 Multiply both sides by 10:(10 (x - 10))/5 = (10 (x + 6))/2 10/5 = (5×2)/5 = 2:2 (x - 10) = (10 (x + 6))/2 10/2 = (2×5)/2 = 5:2 (x - 10) = 5 (x + 6) Expand out terms of the left hand side:2 x - 20 = 5 (x + 6) Expand out terms of the right hand side:2 x - 20 = 5 x + 30 Subtract 5 x from both sides:(2 x - 5 x) - 20 = (5 x - 5 x) + 30 2 x - 5 x = -3 x:-3 x - 20 = (5 x - 5 x) + 30 5 x - 5 x = 0:-3 x - 20 = 30 Add 20 to both sides:(20 - 20) - 3 x = 20 + 30 20 - 20 = 0:-3 x = 30 + 20 30 + 20 = 50:-3 x = 50 Divide both sides of -3 x = 50 by -3:(-3 x)/(-3) = 50/(-3) (-3)/(-3) = 1:x = 50/(-3) Multiply numerator and denominator of 50/(-3) by -1:Answer: x = (-50)/3
