Problem 1. Solve for x: 4 x + 3 = 19 Subtract 3 from both sides: 4 x + (3 - 3) = 19 - 3 3 - 3 = 0: 4 x = 19 - 3 19 - 3 = 16: 4 x = 16 Divide both sides of 4 x = 16 by 4: (4 x)/4 = 16/4 4/4 = 1: x = 16/4 The gcd of 16 and 4 is 4, so 16/4 = (4×4)/(4×1) = 4/4×4 = 4: Answer: x = 4
Problem 2.
Solve for x: (4 x)/3 + 5 = 17 Put each term in (4 x)/3 + 5 over the common denominator 3: (4 x)/3 + 5 = (4 x)/3 + 15/3: (4 x)/3 + 15/3 = 17 (4 x)/3 + 15/3 = (4 x + 15)/3: (4 x + 15)/3 = 17 Multiply both sides of (4 x + 15)/3 = 17 by 3: (3 (4 x + 15))/3 = 3×17 (3 (4 x + 15))/3 = 3/3×(4 x + 15) = 4 x + 15: 4 x + 15 = 3×17 3×17 = 51: 4 x + 15 = 51 Subtract 15 from both sides: 4 x + (15 - 15) = 51 - 15 15 - 15 = 0: 4 x = 51 - 15 51 - 15 = 36: 4 x = 36 Divide both sides of 4 x = 36 by 4: (4 x)/4 = 36/4 4/4 = 1: x = 36/4 The gcd of 36 and 4 is 4, so 36/4 = (4×9)/(4×1) = 4/4×9 = 9: Answer: x = 9
Problem 3
Solve for x: 4 (6 - 2) x - 10 = 20 6 - 2 = 4: 4×4 x - 10 = 20 4×4 = 16: 16 x - 10 = 20 Add 10 to both sides: 16 x + (10 - 10) = 10 + 20 10 - 10 = 0: 16 x = 20 + 10 20 + 10 = 30: 16 x = 30 Divide both sides of 16 x = 30 by 16: (16 x)/16 = 30/16 16/16 = 1: x = 30/16 The gcd of 30 and 16 is 2, so 30/16 = (2×15)/(2×8) = 2/2×15/8 = 15/8: Answer: x = 15/8
Problem 4
Solve for x: 4.3 x + 0.7 = 5 Subtract 0.7 from both sides: 4.3 x + (0.7 - 0.7) = 5 - 0.7 0.7 - 0.7 = 0: 4.3 x = 5 - 0.7 5 - 0.7 = 4.3: 4.3 x = 4.3 Divide both sides of 4.3 x = 4.3 by 4.3: (4.3 x)/4.3 = 4.3/4.3 4.3/4.3 = 1: x = 4.3/4.3 4.3/4.3 = 1: Answer: x = 1 As for the Real world question, I have no idea. Given are, $25 to turn on the electricity and $4/hr to run it. What is she selling and for how much? I don't think there is a solution as not enough information is given.
