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 problems: Problem 1: 2x + 3 = 1x Step 1: Subtract 2x from both sides of the equation. 3 = 1x - 2x Step 2: Combine the x terms. 3 = -x Step 3: Divide both sides by -1 to solve for x. (3)/(-1) = (-x)/(-1) x = -3 The student's solution is correct. x = -3 Problem 2: 2a + 3 = 7x - 6 Step 1: Add 6 to both sides of the equation to isolate the term with x. 2a + 3 + 6 = 7x 2a + 9 = 7x Step 2: Divide both sides by 7 to solve for x. (2a + 9)/(7) = x x = (2a + 9)/(7) x = (2a + 9)/(7) Problem 3: 6x - 5 < 8x Step 1: Subtract 6x from both sides of the inequality. -5 < 8x - 6x -5 < 2x Step 2: Divide both sides by 2. (-5)/(2) < (2x)/(2) -(5)/(2) < x This can also be written as x > -(5)/(2). The student made an error by flipping the inequality sign when dividing by a positive number (2), and also by moving the constant to the wrong side initially. When dividing by a positive number, the inequality sign does not flip. x > -(5)/(2) Problem 4: (3x+5)/(2) (6x+1)/(2) Step 1: Multiply both sides of the inequality by 2 to eliminate the denominators. 2 × (3x+5)/(2) 2 × (6x+1)/(2) 3x+5 6x+1 Step 2: Subtract 3x from both sides. 5 6x - 3x + 1 5 3x + 1 Step 3: Subtract 1 from both sides. 5 - 1 3x 4 3x Step 4: Divide both sides by 3. (4)/(3) (3x)/(3) (4)/(3) x This can also be written as x (4)/(3). The student made an error in their third line of working, where they incorrectly multiplied terms by 2 again. x (4)/(3) Send me the next one 📸