$$ 10 = -9a + 18a + 4 \implies 10 = 9a + 4 \implies 9a = 6 \implies a = rac{2}{3}. $$
["Understanding the Equation: $$ $10 = -9a + 18a + 4 \rightarrow a = \frac{2}{3} $$", "Solving simple linear equations is a fundamental skill in algebra, and equations like $$ 10 = -9a + 18a + 4 $$ appear frequently in school math problems and real-world applications. This article breaks down step-by-step how to solve the equation $$ 10 = -9a + 18a + 4 $$ to find $ a = \frac{2}{3} $, helping students master basic algebra and build strong problem-solving skills.", "---", "### Step 1: Simplify the Equation", "Start with the original equation:\n$$\n10 = -9a + 18a + 4\n$$", "Combine like terms on the right-hand side:\n$$\n-9a + 18a = 9a\n\Rightarrow 10 = 9a + 4\n$$", "This simplifies the expression cleanly to:\n$$\n10 = 9a + 4\n$$", "---", "### Step 2: Isolate the Variable Term", "To solve for $ a $, first subtract 4 from both sides:\n$$\n10 - 4 = 9a\n\Rightarrow 6 = 9a\n$$", "Now the equation reads:\n$$\n9a = 6\n$$", "---", "### Step 3: Solve for $ a $", "Divide both sides by 9:\n$$\na = \frac{6}{9} = \frac{2}{3}\n$$", "Thus, $ a = \frac{2}{3} $ is the solution.", "---", "### Why This Equation Matters", "Linear equations such as $$ 10 = -9a + 18a + 4 $$ model real-life scenarios including budgeting, profit calculations, and physics problems. Mastering how to simplify and isolate variables enables students to tackle complex math and apply algebra confidently in everyday and academic settings.", "---", "### Summary", "The solution steps are clear and straightforward:\n1. Combine like terms: $$ -9a + 18a = 9a $$\n2. Simplify constants: $$ 10 - 4 = 6 $$\n3. Isolate $ a $: $$ 9a = 6 $$\n4. Solve: $$ a = \frac{2}{3} $$", "Knowing how to solve equations like $ 10 = -9a + 18a + 4 $ strengthens algebraic intuition and prepares you for higher-level math challenges.", "---", "Key Takeaway:\nSolve step-by-step—simplify, isolate, solve—and always verify your answer.\nWhen $$ 10 = -9a + 18a + 4 $$ simplifies correctly, you’ll always find $ a = \frac{2}{3} $.", "---", "Keywords: \nLinearEquations #Algebra #SolveForA #MathSolving #$ a = \frac{2}{3} $, stepbystep, equation solutions, algebra tutorial, how to solve equations, simplify linear expressions, math education", "Meta Description:\nLearn step-by-step how to solve $$$10 = -9a + 18a + 4$$ $$, arriving at the solution $ a = \frac{2}{3} $. A clear tutorial for students and math learners."]
