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 for the linear equations: a) Solve 10x - 1 = 15 - 6x Step 1: Add 6x to both sides of the equation. 10x - 1 + 6x = 15 - 6x + 6x 16x - 1 = 15 Step 2: Add 1 to both sides of the equation. 16x - 1 + 1 = 15 + 1 16x = 16 Step 3: Divide both sides by 16. (16x)/(16) = (16)/(16) x = 1 Step 4: Check the solution by substituting x=1 into the original equation. 10(1) - 1 = 15 - 6(1) 10 - 1 = 15 - 6 9 = 9 The solution is correct. The solution for a) is x=1. b) Solve (3x)/(2) + 5 = (5x)/(2) - 1 Step 1: Multiply the entire equation by 2 to eliminate the denominators. 2 ((3x)/(2) + 5) = 2 ((5x)/(2) - 1) 3x + 10 = 5x - 2 Step 2: Subtract 3x from both sides of the equation. 3x + 10 - 3x = 5x - 2 - 3x 10 = 2x - 2 Step 3: Add 2 to both sides of the equation. 10 + 2 = 2x - 2 + 2 12 = 2x Step 4: Divide both sides by 2. (12)/(2) = (2x)/(2) 6 = x Step 5: Check the solution by substituting x=6 into the original equation. (3(6))/(2) + 5 = (5(6))/(2) - 1 (18)/(2) + 5 = (30)/(2) - 1 9 + 5 = 15 - 1 14 = 14 The solution is correct. The solution for b) is x=6. Send me the next one 📸