Substitute into the first equation: \( 3x + 4(2x - 3) = 10 \).
["SEO Optimized Article: Solving Substitution in Algebra: Substitute into the First Equation", "---", "Understanding How to Substitute into the First Equation: ( 3x + 4(2x - 3) = 10 )", "When solving linear equations like ( 3x + 4(2x - 3) = 10 ), one effective technique is substitution — a method that simplifies complex expressions by replacing parts of the equation with simpler forms. In this article, we’ll explore how substitution transforms this equation into a straightforward step-by-step solution. Whether you’re a student learning algebra or a teacher guiding students, mastering substitution boosts your problem-solving skills.", "### Why Substitute?\nSubstitution helps break down complicated expressions by replacing subexpressions with single values or simplified forms. In our equation, ( 2x - 3 ) appears twice: once directly inside parentheses and again wrapped by ( 4(\ ) ). By substituting ( 2x - 3 ) with a temporary variable, we eliminate duplication and reduce the chance of errors.", "### Step-by-Step Guide to Substituting in This Equation", "Step 1: Identify the Subexpression to Substitute\nNotice that ( 2x - 3 ) is the core inner expression. Let’s define:\n[\nu = 2x - 3\n]\nThis substitution replaces every occurrence of ( 2x - 3 ) with ( u ), turning the original equation into:\n[\n3x + 4u = 10\n]", "Step 2: Keep ( x ) in Terms of ( u ) (if needed)\nSince ( u = 2x - 3 ), solve for ( x ):\n[\nu + 3 = 2x \implies x = \frac{u + 3}{2}\n]\nNow substitute this back into the equation:\n[\n3\left( \frac{u + 3}{2} \right) + 4u = 10\n]", "Step 3: Simplify the Equation\nMultiply through:\n[\n\frac{3(u + 3)}{2} + 4u = 10\n]\n[\n\frac{3u + 9}{2} + 4u = 10\n]\nMultiply every term by 2 to eliminate the denominator:\n[\n3u + 9 + 8u = 20\n]\nCombine like terms:\n[\n11u + 9 = 20\n]", "Step 4: Solve for ( u )\nSubtract 9:\n[\n11u = 11\n]\nDivide by 11:\n[\nu = 1\n]", "Step 5: Substitute Back for ( x )\nRecall ( u = 2x - 3 ):\n[\n1 = 2x - 3 \implies 2x = 4 \implies x = 2\n]", "### Final Answer\nThe solution to ( 3x + 4(2x - 3) = 10 ) is ( x = 2 ). Using substitution simplified the original equation by reducing it to a single-variable form, making it easier to solve accurately.", "### SEO Keywords to Optimize This Article:\nSubstitute equation algebra, solve 3x + 4(2x - 3) = 10, algebra substitution method, step-by-step equation solving, simplify linear equation with substitution, algebra substitution examples, how to substitute variable in equations, solve for x algebraically, step 2 substitution technique.", "---", "Conclusion:\nMastering substitution in equations like ( 3x + 4(2x - 3) = 10 ) transforms complexity into clarity. Practice replacing subexpressions and solving stepwise — your algebra skills will improve quickly!", "---", "By implementing substitution strategically, solving linear equations becomes more intuitive, accurate, and manageable — key tools for academic success in mathematics.", "---", "Tag: algebra, substitute in equations, linear equations, solve algebra, step-by-step solving, substitution method, math tutorial, substitute variable, equation solving technique"]
