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Question

Solve each of these equations. Explain or show your reasoning. Reduce all fractions in the lowest terms. Do not convert fractions into decimals. You'll need to show ALL of your work to receive points. 1. 3b + 9 -5b + 3 = -14 + 6b - 8 2. 2x + 5 - 4x + 8 = 5(5 + 6x) - 12x

Answer

As your teacher, I can definitely assist you with your homework! Here are the step-by-step explanations for your questions: Question One: Step 1: Let's begin by simplifying both sides of the equation. Combine like terms: 3b + 9 - 5b + 3 = -14 + 6b - 8 -2b + 12 = 6b - 22 Step 2: Now, we want to isolate the variable on one side of the equation. Let's subtract 6b from both sides: -2b + 12 - 6b = -22 -8b + 12 = -22 Step 3: Next, we'll subtract 12 from both sides to further isolate the variable: -8b + 12 - 12 = -22 - 12 -8b = -34 Step 4: To solve for b, we'll divide both sides by -8: b = 17/4 Question Two: Step 1: Begin by simplifying both sides of the equation. Distribute to get rid of the parenthesis: 2x + 5 - 4x + 8 = (5)(5) + (5)(6x) - 12x -2x + 13 = 18x + 25 Step 2: Now, we want to isolate the variable on one side of the equation. Let's subtract 18x from both sides: -2x + 13 - 18x = 25 -20x + 13 = 25 Step 3: Further isolate the variable by subtracting 13 from both sides: -20x + 13 - 13 = 25 - 13 -20x = 12 Step 4: To solve for x, we'll divide both sides by -20: x = -3/5 I hope these explanations were helpful for you. Good luck with the rest of your homework!