Divide both sides by $-2$:
["How to Divide Both Sides by $-2$: A Step-by-Step Guide for Algebraic Equations", "When working with algebraic equations, one of the fundamental operations is dividing both sides of an equation by a number. But what happens if that number is $-2$? Dividing both sides by $-2$ is a common step in solving equations, especially when simplifying or isolating variables. In this article, we’ll explore how to correctly divide both sides by $-2$, including key rules and practical examples to help you master this essential algebraic skill.", "---", "### Why Divide Both Sides by $-2$?", "Division is the inverse of multiplication, and dividing both sides of an equation by the same non-zero number keeps the equation balanced. Dividing by $-2$ often appears when simplifying equations with negative integers or fractions. Understanding this process ensures accurate solutions and builds confidence in handling negative values in algebra.", "---", "### Step-by-Step: Dividing Both Sides by $-2$", "Here’s how to divide both sides of an equation by $-2$ properly:", "1. Start with your equation\n For example, solve for ( x ):\n [\n -2x = 10\n ]", "2. Divide both sides by $-2$\n [\n \frac{-2x}{-2} = \frac{10}{-2}\n ]", "3. Simplify\n The negatives cancel on the left side, and division yields:\n [\n x = -5\n ]", "This confirms the solution $ x = -5 $ is correct.", "---", "### Key Rule: Sign Change When Dividing by a Negative", "Important:\nSince we divided by $-2$ (a negative number), the sign of the result flips.\n- A positive divided by a negative equals a negative.\n- A negative divided by a negative equals a positive.", "This sign rule applies regardless of the value on either side.", "---", "### Practical Example", "Equation:\n[\n-2(x + 3) = 8\n]", "Step 1: Expand the left side:\n[\n-2x - 6 = 8\n]", "Step 2: Add 6 to both sides:\n[\n-2x = 14\n]", "Step 3: Divide both sides by $-2$:\n[\nx = \frac{14}{-2} = -7\n]", "Check: Substitute $ x = -7 $ back into the original equation:\n[\n-2(-7 + 3) = -2(-4) = 8 \quad \ ext{✓}\n]", "---", "### Common Mistakes to Avoid", "- Forgetting the sign change: Dividing by $-2$ without changing the sign leads to incorrect solutions.\n- Dividing only one side: Always apply the division to both sides to maintain equality.\n- Ignoring absolute values: The magnitude determines the result, regardless of the sign.", "---", "### Conclusion", "Dividing both sides of an equation by $-2$ is a straightforward yet critical algebraic operation. By remembering to flip the sign and divide evenly, you can solve equations confidently and accurately. Whether you're simplifying linear equations or balancing expressions, mastering this step strengthens your algebraic skills and prepares you for more advanced math.", "Start practicing today—divide both sides by $-2$ with ease and build stronger problem-solving habits!", "---", "Keywords: divide both sides by −2, algebraic equations, negating numbers, solving linear equations, algebra step-by-step, math basics, dividing by negative, how to solve equations"]
