Simplify: \( 3x + 10x - 14 = 12 \) leads to \( 13x = 26 \).

["# Simplify: How Solving ( 3x + 10x - 14 = 12 ) Leads Directly to ( 13x = 26 )", "When solving linear equations, simplifying the expression step by step is crucial for reaching the correct solution. One classic example is the equation:", "[\n3x + 10x - 14 = 12\n]", "At first glance, combining like terms simplifies this equation into a clean, solvable form. This process not only demonstrates algebraic skill but also highlights how logical reasoning transforms complexity into clarity. Let’s break down how this equation leads directly to ( 13x = 26 ).", "---", "### Step 1: Combine Like Terms", "The left side of the equation contains two terms with the variable ( x ): ( 3x ) and ( 10x ). These terms are like terms because they both involve ( x ), so they can be combined:", "[\n3x + 10x = 13x\n]", "Substituting this back into the equation gives:", "[\n13x - 14 = 12\n]", "---", "### Step 2: Isolate the Variable Term", "To solve for ( x ), isolate the term containing ( x ). Begin by eliminating the constant on the left side. Add 14 to both sides of the equation:", "[\n13x - 14 + 14 = 12 + 14\n]", "Simplifying both sides yields:", "[\n13x = 26\n]", "---", "### Step 3: Solution", "Now the equation is simplified to ( 13x = 26 ), a straightforward linear form ready for solving by dividing both sides by 13:", "[\nx = \frac{26}{13} = 2\n]", "---", "### Why This Simplification Matters", "Simplifying equations step by step avoids errors and builds mathematical intuition. By recognizing and combining like terms early—here ( 3x + 10x = 13x )—and then isolating the variable, we transform a multi-step expression into a clear target for the next move: solving for ( x ).", "This process exemplifies fundamental algebra skills every student and learner should master. Whether studying for exams, teaching basic algebra, or reinforcing problem-solving techniques, understanding how equations like ( 3x + 10x - 14 = 12 ) reduce cleanly to ( 13x = 26 ) strengthens logical thinking and algebraic fluency.", "---", "### Conclusion", "Solving ( 3x + 10x - 14 = 12 ) leads naturally to ( 13x = 26 ) through proper combination of like terms and isolation of ( x ). This step-by-step simplification is not just a mechanical process—it’s a powerful method for mastering linear equations and building confidence in algebraic reasoning. Keep simplifying, isolating, and solving: the path to clarity is always within reach.", "---", "Keywords for SEO:\nsimplify linear equations, solve 3x + 10x - 14 = 12, algebraic simplification steps, how to solve linear equations, combining like terms, solve for x, step-by-step algebra, equation solving tutorial, simplifying expressions algebraically, step-by-step equation solving."]