Subtract 4 from both sides: \( 3x + 4 - 4 = 19 - 4 \), which simplifies to \( 3x = 15 \).
["How Subtracting 4 from Both Sides Simplifies the Equation: A Step-by-Step Guide", "Solving linear equations is a fundamental skill in algebra, and one of the most helpful techniques is eliminating constants by performing the same operation on both sides of the equation. In this article, we’ll walk through a key step in equation solving: subtracting 4 from both sides, illustrated by the equation:", "[\n3x + 4 - 4 = 19 - 4\n]", "### Step-by-Step Breakdown", "Start with the original equation:", "[\n3x + 4 - 4 = 19 - 4\n]", "#### Step 1: Simplify Both Sides\nOn the left-hand side, observe that ( +4 - 4 ) cancels out:", "[\n3x + (4 - 4) = 3x + 0 = 3x\n]", "On the right-hand side, simplify ( 19 - 4 ):", "[\n19 - 4 = 15\n]", "Now the equation becomes:", "[\n3x = 15\n]", "This simplification is a direct application of subtracting 4 from both sides of the original equation, maintaining balance and solving for ( x ).", "### Why Subtracting 4 from Both Sides Works", "In algebra, the equality principle states that performing the same operation on both sides of an equation preserves equality. By subtracting 4 from both sides, we eliminate the constants on the left side, making the equation cleaner and easier to solve.", "This technique is particularly useful when isolating the variable term and is often a first step in solving more complex equations involving linear expressions.", "### Solving for ( x )", "To find ( x ), divide both sides by 3:", "[\nx = \frac{15}{3} = 5\n]", "### Conclusion", "Subtracting 4 from both sides simplifies the equation from ( 3x + 4 - 4 = 19 - 4 ) to ( 3x = 15 ), a critical step toward solving for ( x ). Mastering this basic operation strengthens your foundation in algebra and empowers you to tackle more advanced problem-solving challenges.", "---", "Key takeaways:\n- Always subtract or add the same value to both sides to maintain equation balance.\n- Simplifying constants helps isolate variables efficiently.\n- This method applies to many linear equations and forms the basis for advanced algebra.", "Keywords: algebra, solving equations, subtract 4, linear equations, isolate variable, equations for kids and students, step-by-step solving, math tips, algebraic manipulation."]
