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, with detailed steps: Problem 1: 2x + 3 = 4x Step 1: Subtract 2x from both sides of the equation to gather x terms on one side. 3 = 4x - 2x Step 2: Combine the x terms. 3 = 2x Step 3: Divide both sides by 2 to solve for x. (3)/(2) = (2x)/(2) x = (3)/(2) Your solution for this problem is correct. x = (3)/(2) Problem 2: 2a + 3 = 7x - 6 Step 1: Add 6 to both sides of the equation to isolate the term containing x. 2a + 3 + 6 = 7x 2a + 9 = 7x Step 2: Divide both sides by 7 to solve for x. (2a + 9)/(7) = (7x)/(7) x = (2a + 9)/(7) x = (2a + 9)/(7) Problem 3: 6x - 5 < 8x Step 1: Subtract 8x from both sides of the inequality to gather x terms on the left. 6x - 8x - 5 < 0 -2x - 5 < 0 Step 2: Add 5 to both sides to move the constant term to the right. -2x < 5 Step 3: Divide both sides by -2. When dividing an inequality by a negative number, you must flip the direction of the inequality sign. (-2x)/(-2) > (5)/(-2) x > -(5)/(2) 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 6x from both sides to gather x terms on the left. 3x - 6x + 5 1 -3x + 5 1 Step 3: Subtract 5 from both sides to move the constant term to the right. -3x 1 - 5 -3x -4 Step 4: Divide both sides by -3. Remember to flip the inequality sign because you are dividing by a negative number. (-3x)/(-3) (-4)/(-3) x (4)/(3) x (4)/(3) That's 2 down. 3 left today — send the next one.