Order the steps for solving the equation: 2x−5=3(4x+5) (8 points) STEP BY STEP

Question

GPT-4o mini · Answer

To solve the equation $ 2x - 5 = 3(4x + 5) $ step by step, follow these steps: 1. **Distribute on the right side**: Start by distributing the $ 3 $ to both terms inside the parentheses on the right side of the equation. $$ 2x - 5 = 3 \cdot 4x + 3 \cdot 5 $$ This simplifies to: $$ 2x - 5 = 12x + 15 $$ 2. **Combine like terms**: Next, we want to isolate $ x $. Start by moving all terms involving $ x $ to one side and the constant terms to the other side. To do this, subtract $ 12x $ from both sides: $$ 2x - 12x - 5 = 15 $$ This simplifies to: $$ -10x - 5 = 15 $$ 3. **Add constant terms**: Now, add $ 5 $ to both sides to move the constant term: $$ -10x - 5 + 5 = 15 + 5 $$ This simplifies to: $$ -10x = 20 $$ 4. **Solve for $ x $**: Finally, divide both sides by $ -10 $ to isolate $ x $: $$ x = \frac{20}{-10} $$ This simplifies to: $$ x = -2 $$ 5. **Check the solution** (optional but recommended): Substitute $ x = -2 $ back into the original equation to verify: $$ 2(-2) - 5 = 3(4(-2) + 5) $$ This simplifies to: $$ -4 - 5 = 3(-8 + 5) $$ Which further simplifies to: $$ -9 = 3(-3) $$ Thus: $$ -9 = -9 \quad \text{(True)} $$ So the solution is $ x = -2 $.