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.
ScanSolve AI Answer
Here are the solutions to the equations using the balancing method: 1. 2x = -10 Step 1: Divide both sides by 2. (2x)/(2) = (-10)/(2) x = -5 The solution is x = -5. 2. 2y = 10 Step 1: Divide both sides by 2. (2y)/(2) = (10)/(2) y = 5 The solution is y = 5. 3. (x)/(9) = -3 Step 1: Multiply both sides by 9. (x)/(9) × 9 = -3 × 9 x = -27 The solution is x = -27. 4. 8 = (p)/(4) Step 1: Multiply both sides by 4. 8 × 4 = (p)/(4) × 4 32 = p The solution is p = 32. 5. 8q - 16 = 0 Step 1: Add 16 to both sides. 8q - 16 + 16 = 0 + 16 8q = 16 Step 2: Divide both sides by 8. (8q)/(8) = (16)/(8) q = 2 The solution is q = 2. 6. z - 8 = 0 Step 1: Add 8 to both sides. z - 8 + 8 = 0 + 8 z = 8 The solution is z = 8. 7. (2x)/(8) = 5 Step 1: Multiply both sides by 8. (2x)/(8) × 8 = 5 × 8 2x = 40 Step 2: Divide both sides by 2. (2x)/(2) = (40)/(2) x = 20 The solution is x = 20. 8. -8 - 5d = 7 Step 1: Add 8 to both sides. -8 - 5d + 8 = 7 + 8 -5d = 15 Step 2: Divide both sides by -5. (-5d)/(-5) = (15)/(-5) d = -3 The solution is d = -3. 9. m + 10 = 16 Step 1: Subtract 10 from both sides. m + 10 - 10 = 16 - 10 m = 6 The solution is m = 6. 10. -k + 7 = 12 Step 1: Subtract 7 from both sides. -k + 7 - 7 = 12 - 7 -k = 5 Step 2: Multiply both sides by -1. -k × (-1) = 5 × (-1) k = -5 The solution is k = -5. That's 2 down. 3 left today — send the next one.