\( 2x + 30 - 3x = 100 \)

["# Solving the Equation ( 2x + 30 - 3x = 100 ): A Step-by-Step Guide", "Understanding how to solve linear equations is essential for mastering algebra. One commonly encountered equation is ( 2x + 30 - 3x = 100 ). This beginner-friendly article breaks down the process of solving this equation, helping you grasp key algebraic concepts and strategies. Whether you're a student learning algebra or a caregiver supporting education, this guide explains everything you need to know.", "## What Is the Equation ( 2x + 30 - 3x = 100 )?", "The equation ( 2x + 30 - 3x = 100 ) is a first-degree linear equation in one variable, ( x ). It combines like terms (the ( x )-terms) and includes constants, making it straightforward to isolate ( x ) and find its value.", "### Step 1: Combine Like Terms\nThe left-hand side contains two ( x )-terms: ( 2x ) and ( -3x ). Combining these:", "[\n2x - 3x + 30 = 100\n]\n[\n(2 - 3)x + 30 = 100\n]\n[\n-x + 30 = 100\n]", "Now, the equation simplifies to:", "[\n-x + 30 = 100\n]", "### Step 2: Isolate the Variable Term\nNext, subtract 30 from both sides to move the constant to the right-hand side:", "[\n-x + 30 - 30 = 100 - 30\n]\n[\n-x = 70\n]", "### Step 3: Solve for ( x )\nTo solve for ( x ), multiply both sides by (-1) to eliminate the negative coefficient:", "[\nx = -70\n]", "### Final Answer\nThe solution to the equation ( 2x + 30 - 3x = 100 ) is:", "[\n\boxed{-70}\n]", "### Verification\nPlugging ( x = -70 ) back into the original equation confirms the solution:", "[\n2(-70) + 30 - 3(-70) = -140 + 30 + 210 = 100\n]", "Since both sides equal ( 100 ), the solution is correct.", "## Why This Equation Matters\nUnderstanding how to solve equations like ( 2x + 30 - 3x = 100 ) builds foundational algebra skills critical for higher-level math, science, and real-world problem solving. Mastery of linear equations supports learning systems of equations, graphing, and functions.", "## Tips for Solving Linear Equations\n- Always combine like terms first.\n- Keep constants on one side and variables on the other.\n- Use inverse operations carefully to isolate the variable.\n- Always verify your solution by substituting it back into the original equation.", "## Conclusion\nSolving ( 2x + 30 - 3x = 100 ) shows that algebra is about systematic steps: combine, simplify, isolate, and check. With practice, equations like this become intuitive, empowering students to tackle more complex problems with confidence.", "---", "Keywords: linear equation, solving (2x + 30 - 3x = 100), algebra tutorial, step-by-step equation solving, how to solve (2x + 30 - 3x = 100), algebraic methods, student resources, math practice, equation simplification."]