-(2x - 5) - (x + 3) = -2x + 5 - x - 3 = -3x + 2 = 12 \Rightarrow -3x = 10 \Rightarrow x = -\frac{10}{3} \approx -3.33

["Understanding and Solving Linear Equations: Step-by-Step Guide with ( -3x = 10 \Rightarrow x = -\frac{10}{3} \approx -3.33 )", "When solving linear equations, accuracy is key — even small arithmetic errors can lead to incorrect solutions. In this article, we’ll break down the step-by-step solution of the equation:", "[\n-(2x - 5) - (x + 3) = -2x + 5 - x - 3 = -3x + 2 = 12\n]\nand explain how we deduce:", "[\n-3x = 10 \quad \Rightarrow \quad x = -\frac{10}{3} \approx -3.33\n]", "---", "### Step 1: Simplify Both Sides of the Equation", "Start with the original equation:\n[\n-(2x - 5) - (x + 3) = -2x + 5 - x - 3\n]", "Distribute the negative signs on the left side:\n[\n-2x + 5 - x - 3\n]", "Now combine like terms:\n- Combine ( -2x - x = -3x )\n- Combine constants ( 5 - 3 = 2 )", "This simplifies the left side to:\n[\n-3x + 2\n]", "So the equation now reads:\n[\n-3x + 2 = -2x + 5 - x - 3\n]", "---", "### Step 2: Finalize Simplification on the Right Side", "Simplify the right-hand side:\n[\n-2x + 5 - x - 3 = (-2x - x) + (5 - 3) = -3x + 2\n]", "Now the equation becomes:\n[\n-3x + 2 = -3x + 2\n]", "---", "### Step 3: Analyze the Result — Is It Correct?", "At first glance, the equation seems trivial:\n[\n-3x + 2 = -3x + 2\n]", "This is actually an identity, meaning it’s true for all values of ( x ). However, the problem gives a downstream result:\n[\n-3x = 10 \Rightarrow x = -\frac{10}{3}\n]", "This suggests the original setup might have been slightly misrepresented or meant to show a step in solving a different equation.", "---", "### Step 4: Revisiting the Problem — Clarifying the Expected Solution Path", "Let’s re-express the problem correctly to align with the expected algebraic steps:", "Suppose the correct simplified equation after combining like terms leads to:\n[\n-(2x - 5) - (x + 3) = 12\n]", "Expanding as before:\n[\n-2x + 5 - x - 3 = 12\n]", "Combine terms:\n[\n-3x + 2 = 12\n]", "Subtract 2 from both sides:\n[\n-3x = 10\n]", "Solve for ( x ):\n[\nx = -\frac{10}{3} \approx -3.33\n]", "---", "### Step 5: Why This Step Matters — Solving Linear Equations", "- Order matters: Always expand parentheses carefully.\n- Combine like terms correctly: Miscombining terms leads to errors.\n- Verify each step: Even simple steps like distributing negatives need attention.\n- Check for identities vs. specific solutions: Not all simplifications lead to unique solutions — some verify consistency.", "---", "### Summary", "- Start with the original equation: ( -(2x - 5) - (x + 3) = -2x + 5 - x - 3 )\n- Expand and simplify both sides to ( -3x + 2 = -3x + 2 ) (identity)\n- To reach ( -3x = 10 ), the equation must be adjusted — e.g., starting from ( -3x + 2 = 12 ) instead\n- Solve: ( -3x = 10 \Rightarrow x = -\frac{10}{3} \approx -3.33 )", "---", "### Final Takeaway", "Mastering linear equations requires precision in expansion, simplification, and step-by-step verification. While some equations reduce to identities (valid for all ( x )), careful analysis ensures accurate solutions when a unique value is expected.", "Use our step-by-step guide to decode future problems — and remember:\n[\n-3x = 10 \Rightarrow x = -\frac{10}{3} \quad \ ext{(approximately } -3.33) \quad \ ext{is correct only when derived from } -3x + 2 = 12.\n]", "---", "Keywords: linear equations, solving equations, algebraic steps, ( -3x = 10 ), solve for ( x ), step-by-step algebra, simplify expressions, math study tips", "If you want, try solving similar equations — and always double-check your simplifications!"]