-3(1 - 2y) + 2z = 5 \Rightarrow -3 + 6y + 2z = 5 \Rightarrow 6y + 2z = 8 \Rightarrow 3y + z = 4

["SEO-Optimized Explanation of Solving the Linear Equation: –3(1 – 2y) + 2z = 5", "---", "### Understanding and Solving the Equation: –3(1 – 2y) + 2z = 5", "Linear equations form the backbone of algebra and are crucial in fields like engineering, economics, and computer science. Today, we break down step-by-step how to solve the equation:\n–3(1 – 2y) + 2z = 5,\nleading through each transformation to the simplified form:\n3y + z = 4. Mastering this process improves your algebraic fluency and problem-solving skills.", "---", "### Step 1: Expand the Parentheses", "Start with the original equation:\n–3(1 – 2y) + 2z = 5", "Apply the distributive property (multiply -3 across the terms inside the parentheses):\n–3 × 1 + (–3 × –2y) + 2z = 5\nWhich simplifies to:\n–3 + 6y + 2z = 5", "---", "### Step 2: Isolate the Constants on One Side", "Move all constant terms to the right side:\nAdd 3 to both sides:\n6y + 2z = 5 + 3\n6y + 2z = 8", "This form makes it easier to further simplify.", "---", "### Step 3: Simplify the Equation", "Divide every term by 2 to reduce coefficients and make the equation cleaner:\n(6y ÷ 2) + (2z ÷ 2) = 8 ÷ 2\n3y + z = 4", "---", "### Final Equation and It’s Meaning", "The simplified equation:\n3y + z = 4", "This is a linear equation with two variables. It represents a line in two-dimensional space and can be used to express ( z ) in terms of ( y ):\nz = 4 – 3y,\nor alternatively, solve for ( y ):\ny = (4 – z) / 3", "Understanding this transformation is essential for modeling relationships between variables in real-world problems.", "---", "### Key Takeaways for Students and Learners", "- Always expand distributive expressions carefully to avoid sign errors.\n- Move constants consistently to isolate variables.\n- Simplify fractions by dividing all terms when possible.\n- Always verify your solution by substituting back into the original equation.", "By mastering algebraic manipulations like these, you strengthen your foundation for advanced math, programming, and technical problem-solving.", "---", "Related Keywords for SEO:\n- How to solve linear equations\n- Step-by-step algebra solving\n- Simplifying equations algebraically\n- Solving –3(1 – 2y) + 2z = 5\n- 3y + z = 4 explanation\n- Linear equation derivation\n- Algebra tips for students", "---", "Optimized for Search Engines:\nThis article targets educational searches such as “how to solve linear equations,” “simplify –3(1 – 2y) + 2z = 5,” and “solve for z in 3y + z = 4.” Including key phrases helps readers find clear, accurate content on mastering algebra step by step.", "---", "Conclusion\nSolving equations like –3(1 – 2y) + 2z = 5 teaches critical algebraic reasoning. The final simplified equation 3y + z = 4 is not just a result—it’s a powerful foundation for further mathematical exploration.", "---", "Author: Math Explained, Algebra Simplified | Keyword density optimized: ~2.5%"]