\[ 14q + 56 + 15q = 105 \]

["# Solve the Equation 14q + 56 + 15q = 105: Step-by-Step Guide", "Are you trying to solve the linear equation 14q + 56 + 15q = 105? You're in the right place! Whether you're a student learning algebra or someone looking to reinforce their math skills, this detailed guide will walk you through solving the equation step by step.", "## Understanding the Equation", "The equation to solve is:", "$$\n14q + 56 + 15q = 105\n$$", "This equation involves combining like terms and isolating the variable q to find its value. It’s a basic linear equation in one variable, commonly encountered in elementary algebra.", "---", "## Step 1: Combine Like Terms", "The terms 14q and 15q are like terms because they both contain the variable q. Combine them:", "$$\n(14q + 15q) + 56 = 105\n$$\n$$\n29q + 56 = 105\n$$", "Now the equation simplifies to:", "$$\n29q + 56 = 105\n$$", "---", "## Step 2: Isolate the Variable Term", "To isolate 29q, subtract 56 from both sides of the equation:", "$$\n29q + 56 - 56 = 105 - 56\n$$\n$$\n29q = 49\n$$", "---", "## Step 3: Solve for q", "Now divide both sides by 29 to solve for q:", "$$\nq = \frac{49}{29}\n$$", "---", "## Final Answer", "$$\n\boxed{q = \frac{49}{29}}\n$$", "---", "## Why This Equation Matters", "Solving equations like 14q + 56 + 15q = 105 helps build essential algebra skills, including:", "- Combining like terms\n- Using the addition and subtraction properties of equality\n- Dividing both sides to isolate variables", "These fundamental skills are crucial for more advanced math topics such as systems of equations, graphing linear functions, and real-world problem solving.", "---", "## Summary", "To solve:\n$$\n14q + 56 + 15q = 105\n$$\n1. Combine like terms: (29q + 56 = 105)\n2. Subtract 56: (29q = 49)\n3. Divide by 29: (q = \frac{49}{29})", "It’s quick, clear, and a perfect example of solving a simple linear equation algebraically.", "---", "Keywords: solve 14q + 56 + 15q = 105, linear equation, algebra solution, step-by-step equation solving, simplified equation, find q, math tutorial, equation practice.", "---", "Want to master algebra? Practice solving similar equations—starting with expressions like this one—and gradually tackle more complex mathematical challenges."]