This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — here are the solutions for the remaining problems: 3. Solve for x: a) Step 1: Combine the constant terms on the left side. x + 3 + 2 = 4 x + 5 = 4 Step 2: Subtract 5 from both sides to isolate x. x + 5 - 5 = 4 - 5 x = -1 The solution is x = -1. b) Step 1: Combine the constant terms on the left side. x + 8 + 7 = -8 x + 15 = -8 Step 2: Subtract 15 from both sides to isolate x. x + 15 - 15 = -8 - 15 x = -23 The solution is x = -23. c) Step 1: Combine the constant terms on the left side. x + 6 + 6 = 3 x + 12 = 3 Step 2: Subtract 12 from both sides to isolate x. x + 12 - 12 = 3 - 12 x = -9 The solution is x = -9. d) Step 1: Combine the constant terms on the left side. x - 9 - 8 = -3 x - 17 = -3 Step 2: Add 17 to both sides to isolate x. x - 17 + 17 = -3 + 17 x = 14 The solution is x = 14. e) Step 1: Combine the constant terms on the left side. x - 5 - 4 = 7 x - 9 = 7 Step 2: Add 9 to both sides to isolate x. x - 9 + 9 = 7 + 9 x = 16 The solution is x = 16. f) Step 1: Combine the constant terms on the left side. x - 11 + 5 = -7 x - 6 = -7 Step 2: Add 6 to both sides to isolate x. x - 6 + 6 = -7 + 6 x = -1 The solution is x = -1. 4. Solve for x: a) Step 1: Divide both sides by 3 to isolate x. 3x = 27 (3x)/(3) = (27)/(3) x = 9 The solution is x = 9. b) Step 1: Combine like terms on the left side. 5x + x = 18 6x = 18 Step 2: Divide both sides by 6 to isolate x. (6x)/(6) = (18)/(6) x = 3 The solution is x = 3. c) Step 1: Add 4 to both sides. 2x - 4 = 10 2x - 4 + 4 = 10 + 4 2x = 14 Step 2: Divide both sides by 2 to isolate x. (2x)/(2) = (14)/(2) x = 7 The solution is x = 7. d) Step 1: Divide both sides by 7 to isolate x. 7x = 28 (7x)/(7) = (28)/(7) x = 4 The solution is x = 4. e) Step 1: Divide both sides by 5 to isolate m. 5m = 25 (5m)/(5) = (25)/(5) m = 5 The solution is m = 5. f) Step 1: Divide both sides by 15 to solve for the product ab. 15ab = 30 (15ab)/(15) = (30)/(15) ab = 2 The solution is ab = 2. 5. Solve for x: a) Step 1: Multiply both sides by 6. (4x)/(6) = 12 6 × (4x)/(6) = 12 × 6 4x = 72 Step 2: Divide both sides by 4 to isolate x. (4x)/(4) = (72)/(4) x = 18 The solution is x = 18. b) Step 1: Multiply both sides by 5 to isolate x. (x)/(5) = 15 5 × (x)/(5) = 15 × 5 x = 75 The solution is x = 75. c) Step 1: Multiply both sides by 2 to isolate x. (x)/(2) = 30 2 × (x)/(2) = 30 × 2 x = 60 The solution is x = 60. d) Step 1: Multiply both sides by 3 to isolate x. (x)/(3) = 6 3 × (x)/(3) = 6 × 3 x = 18 The solution is x = 18. e) Step 1: Multiply both sides by 3 to isolate x. (x)/(3) = 24 3 × (x)/(3) = 24 × 3 x = 72 The solution is x = 72. f) Step 1: Multiply both sides by 7 to isolate x. (x)/(7) = 7 7 × (x)/(7) = 7 × 7 x = 49 The solution is x = 49. Problem solving: Step 1: Write the problem as an equation. "a divided by 25 equals 100" can be written as: (a)/(25) = 100 Step 2: Multiply both sides by 25 to isolate a. 25 × (a)/(25) = 100 × 25 a = 2500 The solution is a = 2500. You've finished all the questions! What's next? 📸