Simplify: \( 3x + 8x - 12 = 10 \) ⟹ \( 11x = 22 \) ⟹ \( x = 2 \).
["# Simplifying Linear Equations: Solve ( 3x + 8x - 12 = 10 ) Step-by-Step", "Solving linear equations is a fundamental skill in algebra, essential for students and math enthusiasts alike. One clear example is simplifying and solving the equation:", "[\n3x + 8x - 12 = 10 \quad \Rightarrow \quad 11x - 12 = 10\n]", "This article will walk you through simplifying the equation step-by-step and arriving at the solution ( x = 2 ). Whether you're learning algebra for school, exams, or personal growth, mastering these steps will build your confidence and accuracy.", "---", "## Step 1: Combine Like Terms on the Left Side", "Start by combining the like terms on the left-hand side. Here, ( 3x ) and ( 8x ) are terms with the variable ( x ):", "[\n3x + 8x - 12 = 10\n]\n[\n(3x + 8x) - 12 = 10\n]\n[\n11x - 12 = 10\n]", "Simplifying gives us a cleaner form:\n( 11x - 12 = 10 )", "---", "## Step 2: Isolate the Variable Term", "To solve for ( x ), first move the constant term (( -12 )) to the right side of the equation. Add 12 to both sides:", "[\n11x - 12 + 12 = 10 + 12\n]\n[\n11x = 22\n]", "This step confirms that the equation now clearly isolates ( 11x ), simplifying further actions.", "---", "## Step 3: Solve for ( x )", "Now that ( 11x = 22 ), divide both sides by 11 to solve for ( x ):", "[\nx = \frac{22}{11} = 2\n]", "Thus, the solution is:\n( x = 2 )", "---", "## Why This Process Works", "Breaking equations into simpler forms by:", "- Combining like terms reduces confusion and error.\n- Isolating variables using inverse operations ensures accurate solutions.\n- Each step maintains equation balance—simplifying on one side requires mirroring on the other.", "---", "## Practice: Apply the Same Technique", "Try solving this similar equation on your own:", "[\n5x + 7x - 3 = 20\n]", "Hint: Combine like terms first, then isolate ( x ).", "---", "## Conclusion", "Understanding How ( 3x + 8x - 12 = 10 ) ⟹ ( 11x = 22 ) ⟹ ( x = 2 ) gives a solid foundation for tackling linear equations. By combining terms and using inverse operations systematically, you’ll simplify complex expressions with ease. Keep practicing—algebra is the key to unlocking higher math!", "---", "### Quick Recap:", "- Combine ( 3x + 8x = 11x )\n- Add 12 to both sides: ( 11x = 22 )\n- Divide by 11: ( x = 2 )", "Mastering these steps is your first step to algebra success!", "---", "Keywords: simplify linear equation, solve 3x + 8x - 12 = 10, algebra step-by-step, linear equations tutorial, mathematical solving techniques, x equals, equation solving steps, school math help, practice algebra."]
