\[ x + 2(10 - 2x) = 8 \] - United Radiology

["Solving the Equation: ( x + 2(10 - 2x) = 8 )", "Solving linear equations is a foundational skill in algebra, essential for students, educators, and anyone looking to strengthen their problem-solving abilities. One commonly encountered type is equations involving parentheses—like ( x + 2(10 - 2x) = 8 ). In this article, we’ll walk through the step-by-step solution, explore key algebraic concepts, and offer practical insights to help you master this equation format.", "---", "### The Equation:
\n[
\nx + 2(10 - 2x) = 8
\n]", "---", "### Step 1: Distribute the 2 Across the Parentheses
\nTo simplify, start by eliminating parentheses using the distributive property:
\n[
\nx + 2 \cdot 10 - 2 \cdot 2x = 8
\n]
\n[
\nx + 20 - 4x = 8
\n]", "Why this step?
\nDistributing ensures every term inside parentheses is multiplied by the factor outside, removing complexity and preparing the equation for combining like terms.", "---", "### Step 2: Combine Like Terms
\nCombine the ( x ) and ( -4x ) terms:
\n[
\n(x - 4x) + 20 = 8
\n]
\n[
\n-3x + 20 = 8
\n]", "Pro Tip: Always group like terms—combining ( x ) and ( -4x ) simplifies future steps and reduces errors.", "---", "### Step 3: Isolate the Variable
\nSubtract 20 from both sides to begin isolating ( x ):
\n[
\n-3x = 8 - 20
\n]
\n[
\n-3x = -12
\n]", "Key Idea: To solve for ( x ), divide both sides by (-3):
\n[
\nx = \frac{-12}{-3} = 4
\n]", "---", "### Step 4: Check the Solution
\nAlways verify by substituting ( x = 4 ) back into the original equation:
\n[
\n4 + 2(10 - 2 \cdot 4) = 4 + 2(10 - 8) = 4 + 2(2) = 4 + 4 = 8
\n]
\n✅ The equation holds true—( x = 4 ) is the correct solution.", "---", "### Why Translating Equations Accurately Matters
\nEquations like ( x + 2(10 - 2x) = 8 ) appear in real-life problems involving budgeting, physics, and data analysis. Mastering their solution develops logical thinking and algebraic fluency—useful not just in math class, but in everyday decision-making.", "---", "### Summary: Quick Steps to Solve
\n1. Distribute any parentheses.
\n2. Combine like terms.
\n3. Isolate the variable using inverse operations.
\n4. Verify your solution by substituting back.", "Mastering these steps enables you to conquer equations like ( x + 2(10 - 2x) = 8 ) with confidence—and ace your algebra exams.", "---", "### Further Reading
\n- How to Fact Apply the Distributive Property
\n- Strategies for Solving Multi-Step Equations
\n- Real-World Applications of Linear Equations", "Need more help with algebra? Explore our guide on mastering linear equations and boost your math skills today!"]