Now substitute \( h = \frac{27}{11} \) back into \( k = 2h - 4 \):

["Understanding the Substitution: Replacing ( h = \frac{27}{11} ) into ( k = 2h - 4 )", "When solving equations, substitution is a powerful technique that allows us to simplify expressions by replacing variables with known values. One common substitution example involves substituting ( h = \frac{27}{11} ) into the linear equation ( k = 2h - 4 ). This article explains how to perform this substitution step-by-step, why it matters, and the simplified result.", "### What Does It Mean to Substitute ( h = \frac{27}{11} ) into ( k = 2h - 4 )?", "Substituting ( h = \frac{27}{11} ) means replacing every instance of ( h ) in the expression ( k = 2h - 4 ) with ( \frac{27}{11} ). This substitution helps eliminate the variable ( h ) and solve directly for ( k ). It’s especially useful in algebra, physics, and engineering problems where expressions depend on multiple variables.", "### Step-by-Step Substitution", "1. Start with the equation:\n [ k = 2h - 4 ]", "2. Substitute ( h = \frac{27}{11} ):\n Replace ( h ) with ( \frac{27}{11} ):\n [ k = 2\left( \frac{27}{11} \right) - 4 ]", "3. Multiply:\n [ k = \frac{2 \ imes 27}{11} - 4 = \frac{54}{11} - 4 ]", "4. Express 4 with a denominator of 11 for common denominators:\n [ 4 = \frac{44}{11} ]", "5. Subtract the fractions:\n [ k = \frac{54}{11} - \frac{44}{11} = \frac{10}{11} ]", "### Final Result", "After substituting and simplifying, we find:\n[ k = \frac{10}{11} ]", "This means when ( h = \frac{27}{11} ), the value of ( k ) becomes ( \frac{10}{11} ), a rational number that plays a key role in equations involving linear relationships with fractional constants.", "### Why This Substitution Is Useful", "- Clearer computation: Converts symbolic expressions into numerical values.\n- Foundation for modeling: Applies to real-world scenarios such as scaling formulas, reciprocal relationships, or proportional changes.\n- Enhances problem-solving clarity: Eliminating variables reduces complexity, enabling faster verification and analysis.", "In summary, substituting ( h = \frac{27}{11} ) into ( k = 2h - 4 ) simplifies neatly to ( k = \frac{10}{11} ). Mastering such substitutions strengthens algebraic fluency and prepares learners for more advanced mathematical challenges.", "---", "This substitution method is fundamental in mathematics and related disciplines—efficiently transforming equations by replacing variables enhances both accuracy and understanding. Whether you're solving equations by hand or using computational tools, mastering substitutions like this lays the groundwork for success."]