Subtract: $ (9a + b) - (6a + b) = 0 - 5 \Rightarrow 3a = -5 \Rightarrow a = -\frac{5}{3} $

["Solving Linear Equations Step-by-Step: $ (9a + b) - (6a + b) = 0 - 5 \Rightarrow 3a = -5 \Rightarrow a = -\frac{5}{3} $", "Understanding how to solve linear equations is a fundamental skill in algebra — and mastering this process offers clear, step-by-step clarity in simplifying and solving expressions. In this article, we break down the equation $(9a + b) - (6a + b) = 0 - 5$, demonstrating how simplification leads directly to solving for $a$. Whether you're a student learning algebra or self-teaching math fundamentals, this process reveals the logical flow behind equations that viele people encounter.", "---", "### The Equation: Simplifying $(9a + b) - (6a + b) = -5$", "Start with the original equation:\n$$(9a + b) - (6a + b) = 0 - 5$$", "First, simplify both sides.", "Left side:\n$$(9a + b) - (6a + b)$$\nDistribute the negative sign:\n$$9a + b - 6a - b$$\nNow combine like terms:\n$$(9a - 6a) + (b - b) = 3a + 0 = 3a$$", "Right side:\n$$0 - 5 = -5$$", "After simplification, the equation becomes:\n$$3a = -5$$", "---", "### Solving for $a$: Isolate the variable", "To solve $3a = -5$, divide both sides by 3:\n$$a = \frac{-5}{3}$$", "This simple yet powerful step isolates $a$, confirming the unique solution consistent with algebraic principles.", "---", "### Why This Matters: Practical Applications of Solving Equations", "Linear equations like this appear in real-world scenarios — from calculating costs and profits in business to modeling physical phenomena. Being able to systematically simplify and solve such equations is essential for anyone studying math, engineering, economics, or science.", "Moreover, this method reinforces critical thinking:\n- Recognizing like terms\n- Managing parentheses and distributive properties\n- Isolating variables through inverse operations", "Each step builds confidence and precision, laying the groundwork for more advanced algebra and calculus concepts.", "---", "### Quick Summary: Key Steps Recap", "1. Expand expressions: $(9a + b) - (6a + b) = 3a$\n2. Simplify right side: $0 - 5 = -5$\n3. Form simplified equation: $3a = -5$\n4. Solve for $a$: $a = -\frac{5}{3}$", "---", "### Final Note", "Mastering this basic yet illustrative problem equips you with the skills to tackle more complex equations. Remember: algebra is logic structured in symbols. With clear, methodical steps, even abstract expressions break down into simple truths. Keep practicing — every subtraction, simplification, and solution brings you closer to fluency in mathematical reasoning.", "---", "Key phrases for SEO optimization:\n- Solve linear equations step-by-step\n- Algebraic simplification and solving\n- How to solve $(9a + b) - (6a + b) = -5$\n- Step-by-step linear equation solution\n- Isolate variable: $a = -\frac{5}{3}$ explained\n- Basic algebra fundamentals tutorial", "Optimize your study or teaching with this foundational equation: $(9a + b) - (6a + b) = 0 - 5 \Rightarrow 3a = -5 \Rightarrow a = -\frac{5}{3}$"]