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: 1. We need to solve the equation (x+1)/(3) + (x+7)/(3) + (x)/(2) = 5. Step 1: Combine the fractions with the same denominator. ((x+1) + (x+7))/(3) + (x)/(2) = 5 (2x+8)/(3) + (x)/(2) = 5 Step 2: Find a common denominator for 3 and 2, which is 6. Multiply the entire equation by 6. 6 ( (2x+8)/(3) ) + 6 ( (x)/(2) ) = 6 × 5 2(2x+8) + 3x = 30 Step 3: Distribute and simplify the equation. 4x + 16 + 3x = 30 7x + 16 = 30 Step 4: Isolate x. 7x = 30 - 16 7x = 14 x = (14)/(7) x = 2 The correct option is 2) 2. The final answer is 2. 2. We need to solve the equation (x)/(3) - (7)/(9) = (20)/(9). Step 1: Add (7)/(9) to both sides of the equation. (x)/(3) = (20)/(9) + (7)/(9) (x)/(3) = (20+7)/(9) (x)/(3) = (27)/(9) Step 2: Simplify the fraction on the right side. (x)/(3) = 3 Step 3: Multiply both sides by 3 to solve for x. x = 3 × 3 x = 9 The correct option is 3) 9. The final answer is 9. 3. We need to solve the equation (3x)/(2) + 4 = 4x - 11. Step 1: Multiply the entire equation by 2 to eliminate the fraction. 2 ( (3x)/(2) + 4 ) = 2(4x - 11) 3x + 8 = 8x - 22 Step 2: Gather x terms on one side and constant terms on the other side. 8 + 22 = 8x - 3x 30 = 5x Step 3: Solve for x. x = (30)/(5) x = 6 The correct option is 3) 6. The final answer is 6. 4. We need to solve the equation 2x - 8 - 3x = x - 12. Step 1: Combine like terms on the left side of the equation. (2x - 3x) - 8 = x - 12 -x - 8 = x - 12 Step 2: Gather x terms on one side and constant terms on the other side. -8 + 12 = x + x 4 = 2x Step 3: Solve for x. x = (4)/(2) x = 2 The correct option is 2) 2. The final answer is 2. 5. We need to solve the equation (7y)/(3) - 4 = (2y)/(6) + 8. Step 1: Simplify the fraction (2y)/(6). (7y)/(3) - 4 = (y)/(3) + 8 Step 2: Multiply the entire equation by 3 to eliminate the fractions. 3 ( (7y)/(3) - 4 ) = 3 ( (y)/(3) + 8 ) 7y - 12 = y + 24 Step 3: Gather y terms on one side and constant terms on the other side. 7y - y = 24 + 12 6y = 36 Step 4: Solve for y. y = (36)/(6) y = 6 The final answer is 6. Send me the next one 📸