\[ (2x + y) + (x - y) = 10 + 2 \]

["Title: Solving the Equation (2x + y) + (x - y) = 10 + 2: Step-by-Step Guide", "Meta Description: Master how to simplify and solve the equation (2x + y) + (x - y) = 10 + 2 with clear, easy-to-follow steps and key formulas.", "---", "## Mastering the Equation (2x + y) + (x - y) = 10 + 2: A Step-by-Step Solution", "When faced with an algebraic equation like (2x + y) + (x - y) = 10 + 2, solving it step-by-step can feel simple—if you know the correct process. Whether you’re a high school student learning algebra or a parent helping with homework, understanding how to simplify and solve this equation unlocks the foundation for more advanced math.", "In this article, we’ll break down the solution to the equation:", "(2x + y) + (x - y) = 10 + 2", "---", "### Step 1: Simplify Both Sides", "Start by simplifying both sides of the equation:", "Left side:\n(2x + y) + (x - y)\n= 2x + y + x - y\n= (2x + x) + (y - y)\n= 3x + 0\n= 3x", "Right side:\n10 + 2\n= 12", "So the equation now simplifies to:", "3x = 12", "---", "### Step 2: Solve for x", "To isolate x, divide both sides of the equation by 3:", "[\n\frac{3x}{3} = \frac{12}{3}\n]", "[\nx = 4\n]", "---", "### Step 3: Note What Can (and Can’t) Be Determined", "While we’ve found that x = 4, the original equation includes the variable y. However, because all y terms canceled out (y − y = 0), the value of y cannot be determined from this equation alone. Thus, the equation has one solution for x, but y remains a free variable.", "---", "### Final Answer", "The solution to (2x + y) + (x - y) = 10 + 2 is:", "- x = 4\n- y is undefined (no unique solution for y)", "---", "### Why This Equation Matters in Algebra", "Algebraic equations like this demonstrate how combining like terms simplifies expressions, and how substitution brings variables to the forefront. This type of problem strengthens skills in:", "- Combining like terms\n- Simplifying expressions\n- Solving linear equations\n- Recognizing parameters and dependent variables", "---", "### Want to Practice Like a Pro?", "Try solving similar equations like:\n(3x + 2y) – (x – y) = 7 + 4\nor\n(5x + 3) + (2x – y) = 18", "Always simplify fully before solving, and remember: cancellation of y in this example often reveals whether y can be determined.", "---", "Key Takeaways:\n- Simplify expressions by combining like terms.\n- Cancel identical variables where possible.\n- After simplifying, isolate the unknown variable.\n- Recognize when a variable cannot be uniquely determined from an equation.", "---", "Keywords: solve (2x + y) + (x - y) = 10 + 2, algebra equation, simplify linear equation, solve for x step-by-step, algebra tutorial, step-by-step math, how to solve equations, linear equations with two variables", "Related Topics:\n- Simplifying algebraic expressions\n- Isolating variables\n- Solving for x in word problems\n- Identifying dependent and independent variables", "---", "Optimized for: improved algebra understanding, step-by-step equation solving, educational resources, algebra homework help, solving linear equations, algebraic simplification.", "---", "If you found this guide helpful, share it with fellow learners—and remember: mastering basic equations like this lays the groundwork for studying calculus, linear algebra, and beyond!"]