["# How to Solve the Equation ( 10 = 20 - 0.10x ) – A Step-by-Step Guide", "Solving linear equations like ( 10 = 20 - 0.10x ) is a fundamental math skill helpful in algebra, finance, science, and everyday problem-solving. Whether you're a student learning algebra basics or someone brushing up on math techniques, understanding how to isolate the variable step-by-step is key.", "## Understanding the Equation", "The equation ( 10 = 20 - 0.10x ) is a linear equation where:", "- ( 10 ) is the constant value on the left side
\n- ( 20 ) is the constant on the right
\n- ( -0.10x ) is the variable term, representing ( $0.10 $x $, often used in real-world contexts like price reduction or depreciation", "Our goal is to solve for ( x ), the unknown variable.", "---", "## Step-by-Step Solution", "### Step 1: Subtract 20 from both sides
\nTo isolate the term involving ( x ), subtract 20 from both sides:", "[
\n10 - 20 = 20 - 0.10x - 20
\n]", "This simplifies to:", "[
\n-10 = -0.10x
\n]", "### Step 2: Divide both sides by (-0.10)
\nNow divide both sides by (-0.10) to solve for ( x ):", "[
\n\frac{-10}{-0.10} = x
\n]", "### Step 3: Calculate the result
\nSimplify the division:", "[
\nx = \frac{-10}{-0.10} = 100
\n]", "---", "## Final Answer", "[
\n\boxed{x = 100}
\n]", "---", "## Why This Equation Matters", "This simple equation models real-life situations such as:", "- Determining discount amounts when a number of items are reduced by a fixed cost per unit
\n- Calculating measurement conversions involving percentage discounts or depreciation rates", "### Example Use Case:
\nImagine you’re shopping for a $20 gadget with a 10% discount. You know the final price is $10. Using the equation (10 = 20 - 0.10x), you solve for (x) (number of discounts applied) and find (x = 100), confirming the discount rate is applied once across multiple units.", "---", "## Tips for Solving Similar Equations", "- Always keep both sides balanced
\n- Perform operations in reverse order (first eliminate constants, then isolate the variable)
\n- Divide only when dividing by a negative number—remember the sign flip
\n- Check your answer by substituting ( x = 100 ) back into the original equation", "[
\n10 = 20 - 0.10(100) \Rightarrow 10 = 20 - 10 \Rightarrow 10 = 10 \quad \ ext{(Valid)}
\n]", "---", "## Further Reading & Resources", "- Algebra for Beginners: Solving Linear Equations
\n- How to Work with Decimal Coefficients in Equations
\n- Real-World Applications of Linear Equations in Finance and Science", "Start mastering linear equations today—solving ( 10 = 20 - 0.10x ) opens doors to more complex math and practical problem solving!"]
