["# Solve the Equation: ( 3x + 100 - 5x = 80 ) – Step-by-Step Guide", "Solving linear equations is a fundamental skill in algebra, and mastering equations like ( 3x + 100 - 5x = 80 ) builds confidence in manipulating expressions and isolating variables. This comprehensive guide walks you through solving the equation step-by-step, explains key algebraic concepts, and offers practical tips for students and lifelong learners.", "---", "## What Is the Equation?", "We begin with the equation:
\n[
\n3x + 100 - 5x = 80
\n]
\nThis expression involves combining like terms, simplifying, and isolating the variable ( x ) using inverse operations.", "---", "## Step 1: Combine Like Terms", "First, simplify the left-hand side by combining the ( x )-terms:", "[
\n(3x - 5x) + 100 = 80
\n]", "[
\n-2x + 100 = 80
\n]", "Why? Combining coefficients (-5x + 3x = -2x) reduces complexity and moves you closer to isolating ( x ).", "---", "## Step 2: Isolate the Variable Term", "To eliminate the constant term ( +100 ), subtract 100 from both sides:", "[
\n-2x + 100 - 100 = 80 - 100
\n]", "[
\n-2x = -20
\n]", "Why? Using the subtraction property of equality keeps the equation balanced while moving all variable terms to one side.", "---", "## Step 3: Solve for ( x )", "Now divide both sides by (-2) to solve for ( x ):", "[
\nx = \frac{-20}{-2} = 10
\n]", "Final Answer: The solution is ( \mathbf{x = 10} ).", "---", "## Why This Equation Matters (Real-World Application)", "Equations like ( 3x + 100 - 5x = 80 ) represent real-life scenarios such as budgeting, physics equations for motion, or profit calculations. Being able to solve them helps model and solve practical problems with precision.", "---", "## Key Algebra Concepts Explained", "- Like Terms: Terms with the same variable raised to the same power (e.g., ( 3x ) and ( -5x )) can be combined.
\n- Subtraction Property of Equality: Subtracting the same value from both sides preserves the equality.
\n- Dividing by a Negative: Special care is needed when dividing by a negative—never changes the inequality direction (though here, equality remains unchanged).", "---", "## Tips for Solving Similar Linear Equations", "1. Always simplify both sides before solving.
\n2. Use inverse operations step-by-step.
\n3. Check your solution by substituting ( x = 10 ) back into the original equation.
\n [
\n 3(10) + 100 - 5(10) = 30 + 100 - 50 = 80 \quad \ ext{✓}
\n ]", "---", "## Summary", "Solving ( 3x + 100 - 5x = 80 ) involves combining like terms, isolating the variable, and applying inverse operations. The solution, ( x = 10 ), confirms that systematic steps and adherence to algebraic rules yield accurate results.", "---", "## Need More Help?", "Explore tutorials on:
\n- How to graph linear equations
\n- Systems of linear equations
\n- Graphing and solving quadratic equations", "Master algebra — it’s your foundation for advanced math!", "---", "Keywords: Solve ( 3x + 100 - 5x = 80 ), linear equation, algebra tutorial, step-by-step solving, isolate variable, algebraic equations, math help for students."]
