Subtract \(2x\) from both sides: \(x + 5 = 15\).
["How to Solve (x + 5 = 15) by Subtracting (2x) from Both Sides", "Solving equations is a fundamental skill in algebra, and one common method involves simplifying both sides to isolate the variable. One effective technique is subtracting (2x) from both sides of an equation—especially when the goal is to eliminate one variable and simplify the expression. In this article, we’ll explore how subtracting (2x) from both sides helps solve the equation (x + 5 = 15), step by step.", "### Understanding the Equation (x + 5 = 15)", "The equation (x + 5 = 15) is a linear equation in one variable, (x). It states that when (x) is added to 5, the result is 15. To solve for (x), we need to perform inverse operations to isolate (x) on one side. While addition and subtraction are commonly used first, subtracting (2x) offers an alternative path, particularly useful in more complex equations.", "### Step-by-Step Guide: Subtracting (2x) from Both Sides", "Step 1: Start with the original equation\n[\nx + 5 = 15\n]", "Step 2: Subtract (2x) from both sides\nSubtracting (2x) from the left side removes the (x) term:\n[\nx + 5 - 2x = 15 - 2x\n]\nSimplify the left-hand side:\n[\n(1x - 2x) + 5 = -x + 5\n]\nSo the equation becomes:\n[\n-x + 5 = 15 - 2x\n]", "Step 3: Rearranging terms\nNow we simplify and arrange terms to have all variable terms on one side or constants on the other. Subtract 5 from both sides:\n[\n-x = 15 - 2x - 5\n]\n[\n-x = 10 - 2x\n]", "Step 4: Add (2x) to eliminate the (x)-term\nAdding (2x) to both sides cancels the (-2x) on the right:\n[\n-x + 2x = 10\n]\n[\nx = 10\n]", "### Why Subtract (2x)? Strategic Insight", "While direct subtraction of (x) from both sides ((x + 5 - x = 15 - x)) is simpler, subtracting (2x) strategically eliminates one side of the variable. This method becomes valuable in multi-step equations or when preparing for factorization. It also reinforces understanding of how inverse operations work across equation transformations.", "### Final Solution", "Solving (x + 5 = 15), we subtracted (2x) from both sides to eliminate the variable term on the left, simplifying the equation into a form where (x) can be directly isolated. The final result is:\n[\nx = 10\n]", "Verification: Plug (x = 10) back into the original equation:\n[\n10 + 5 = 15 \quad \ ext{(True)}\n]", "### Conclusion", "Although not the simplest path, subtracting (2x) from both sides demonstrates a key algebraic strategy—manipulating equations using inverse operations. Practice this technique in varied equations to strengthen your fluency in solving linear equations.", "---", "Keywords: solve equations, subtract (2x), algebra, linear equations, isolate variable, step-by-step solving, (x + 5 = 15), equation solving tips.", "Meta Description: Learn how subtracting (2x) from both sides helps solve (x + 5 = 15). Follow a clear step-by-step method with verification and strategic insight."]
