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.
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You're on a roll — Here are the solutions to the assignment problems: 1) Step 1: Write the given equation. 2x + 1 = 7x + 3 Step 2: Subtract 2x from both sides. 1 = 5x + 3 Step 3: Subtract 3 from both sides. -2 = 5x Step 4: Divide by 5. x = -(2)/(5) The solution is x = -(2)/(5) 2) Step 1: Write the given equation. 8 - 3x = 2x - 5 Step 2: Add 3x to both sides. 8 = 5x - 5 Step 3: Add 5 to both sides. 13 = 5x Step 4: Divide by 5. x = (13)/(5) The solution is x = (13)/(5) 3) Step 1: Write the given equation. 5(a - 1) = 3(2a + 1) Step 2: Distribute the numbers on both sides. 5a - 5 = 6a + 3 Step 3: Subtract 5a from both sides. -5 = a + 3 Step 4: Subtract 3 from both sides. -8 = a The solution is a = -8 4) Step 1: Write the given equation. 2(x + 5) = 4 - x Step 2: Distribute the 2 on the left side. 2x + 10 = 4 - x Step 3: Add x to both sides. 3x + 10 = 4 Step 4: Subtract 10 from both sides. 3x = -6 Step 5: Divide by 3. x = -2 The solution is x = -2 5) Step 1: Write the given equation. 4(3 - 5y) = -7(5 - 4y) Step 2: Distribute the numbers on both sides. 12 - 20y = -35 + 28y Step 3: Add 20y to both sides. 12 = -35 + 48y Step 4: Add 35 to both sides. 47 = 48y Step 5: Divide by 48. y = (47)/(48) The solution is y = (47)/(48) Drop the next question.