Substitute into the first equation: \( 3x + 2(5x - 7) = 12 \).

["Title: How to Substitute the First Equation: Solve ( 3x + 2(5x - 7) = 12 ) Step by Step", "When solving equations in algebra, substitution is a powerful technique that helps simplify complex expressions. In this SEO-friendly guide, we’ll walk you through substituting into the first equation for ( 3x + 2(5x - 7) = 12 ), showing how substitution streamlines equation solving.", "---", "### Introduction", "Working with equations like ( 3x + 2(5x - 7) = 12 ) often requires transforming parts of the expression to solve for ( x ). One effective method is substitution—replacing a section of the equation with a single expression to simplify the problem. In this case, substituting ( 5x - 7 ) lets us rewrite the equation more clearly.", "---", "### Step 1: Identify the part to substitute", "The expression inside the parentheses, ( 5x - 7 ), appears twice and is multiplied by 2. This makes it a clear candidate for substitution. Let’s define:", "[\nu = 5x - 7\n]", "Substituting ( u ) into the original equation gives:", "[\n3x + 2u = 12\n]", "Now the equation uses both ( x ) and ( u ), making it simpler to manage—especially if we later solve for ( u ) first.", "---", "### Step 2: Express ( x ) in terms of ( u ) (optional)", "If needed, we can reverse the substitution to express ( x ) as a function of ( u ):", "[\nu = 5x - 7 \Rightarrow x = \frac{u + 7}{5}\n]", "But for now, substituting directly into the equation is sufficient.", "---", "### Step 3: Substitute back into the original equation", "Replace ( 2(5x - 7) ) with ( 2u ):", "[\n3x + 2u = 12\n]", "Now recall ( u = 5x - 7 ), but we keep the substitution for clarity.", "---", "### Step 4: Solve for ( u )", "We now have an equation in terms of ( x ) and ( u ). However, since ( u = 5x - 7 ), we proceed by substituting ( x ) in terms of ( u ) or solving the simplified equation.", "Let’s use the expression:", "[\n3x = 12 - 2u \Rightarrow x = \frac{12 - 2u}{3}\n]", "But since ( u = 5x - 7 ), substitute this back:", "[\nx = \frac{12 - 2(5x - 7)}{3}\n]", "This confirms our substitution transformed the original equation correctly.", "---", "### Step 5: Solve for ( x )", "Now substitute ( u = 5x - 7 ) directly into the original:", "[\n3x + 2(5x - 7) = 12\n]", "Expand the parentheses:", "[\n3x + 10x - 14 = 12\n]", "Combine like terms:", "[\n13x - 14 = 12\n]", "Add 14 to both sides:", "[\n13x = 26\n]", "Divide by 13:", "[\nx = 2\n]", "---", "### Bonus: Verify by substitution", "Plug ( x = 2 ) into the original equation:", "[\n3(2) + 2(5(2) - 7) = 6 + 2(10 - 7) = 6 + 2(3) = 6 + 6 = 12\n]", "Confirmed! The solution satisfies the equation.", "---", "### Why Substitution Works", "Substituting parts of expressions into single variables—like replacing ( 5x - 7 ) with ( u )—simplifies equations by reducing terms and clarifying dependencies between variables. This technique improves readability and step-by-step accuracy in solving complex algebraic equations.", "---", "### Conclusion", "Mastering substitution in equations like ( 3x + 2(5x - 7) = 12 ) makes solving easier and more efficient. By identifying repetitive expressions, replacing them with concise variables, and carefully substituting back, you simplify the solving process. Whether you're learning algebra or brushing up on techniques, substitution is a valuable tool for equation mastery.", "---", "Keywords: solve algebra equations, substitution method, ( 3x + 2(5x - 7) = 12 ), equation solving step-by-step, algebra tutorial, simplify equations, substitution in algebra", "---", "Meta Description:\nLearn how to substitute and solve ( 3x + 2(5x - 7) = 12 ) step by step. Learn algebra techniques, simplify expressions, and master substitution for clearer equation solving. Perfect for students and math learners.", "---", "Internally Linked Terms:\n- Practice: Solve linear equations with substitution\n- Algebra fundamentals\n- Steps to solve equations with parentheses", "---", "Call to Action:\nWant more tips on algebraic methods? Try solving ( 4x - 3(2x + 1) = 5 ) using substitution—just like above!"]