\[ (x + y) + (x - y) = 10 + 4 \]

["Title: Solving (x + y) + (x - y) = 10 + 4: A Step-by-Step Guide to Simplify and Solve", "Meta Description:\nLearn how to simplify and solve the equation ((x + y) + (x - y) = 10 + 4) step by step. Discover algebraic techniques, understand key simplifications, and master solving linear equations in two variables.", "---", "### Simplifying and Solving ((x + y) + (x - y) = 10 + 4)", "In algebra, understanding how to simplify and solve equations is essential—whether you're working on homework, preparing for exams, or building foundational skills. One common task is solving equations involving expressions with two variables, such as:", "[\n(x + y) + (x - y) = 10 + 4\n]", "This equation combines linear expressions for both (x) and (y), and with clear steps, you can simplify and find possible values for (x) and (y).", "---", "### Step 1: Simplify Both Sides of the Equation", "Start by simplifying the left-hand side ((x + y) + (x - y)):", "[\n(x + y) + (x - y) = x + y + x - y\n]", "Combine like terms:", "[\nx + x + y - y = 2x + 0 = 2x\n]", "Now simplify the right-hand side:", "[\n10 + 4 = 14\n]", "So the equation becomes:", "[\n2x = 14\n]", "---", "### Step 2: Solve for (x)", "Divide both sides by 2:", "[\nx = \frac{14}{2} = 7\n]", "At this point, we’ve determined that (x = 7). Notice that in the original equation, (y) canceled out—meaning the equation gives no specific information about (y).", "---", "### Step 3: Express the Solution", "Since (y) does not appear in the final simplified form, (y) is a free variable—any real number satisfies the original equation as long as (x = 7).", "So the solution set is:", "[\nx = 7,\quad y \in \mathbb{R}\n]", "---", "### Why Understanding This Matters (SEO Relevance)", "Mastering how to combine terms, simplify both sides, and isolate variables is vital for solving more complex systems of equations. This concept forms the basis for linear programming, graphing equations, and real-world applications like budgeting or physics.", "---", "### Summary", "- Simplify ((x + y) + (x - y)) to (2x).\n- Simplify (10 + 4) to (14).\n- Express the equation as (2x = 14).\n- Solve to find (x = 7), with (y) unrestricted.\n- Ideal for beginners learning algebraic manipulation and equation solving.", "---", "### Key SEO Keywords:\nsolve (x + y) + (x - y) = 10 + 4, simplify linear equation, solve for x and y, algebraic equation solving, two variable equations, step-by-step algebra, linear equation solve, free variable in equations", "---", "Start building your algebra skills today—simplify, solve, and solve again with clarity."]