\[ = rac{1}{2} \left| 1(3) + 4(1) + 5(-4)

["Understanding and Simplifying the Expression:\n[ = \frac{1}{2} \left| 1(3) + 4(1) + 5(-4) \right|", "---", "Simplifying Step-by-Step\nWhen working with expressions involving absolute value and multiplication, it’s essential to simplify inside the parentheses before applying the absolute value or other operations.", "Start with:\n[ 1(3) + 4(1) + 5(-4) ]", "Calculate each term:\n- (1 \ imes 3 = 3)\n- (4 \ imes 1 = 4)\n- (5 \ imes (-4) = -20)", "Now add them together:\n[ 3 + 4 + (-20) = 7 - 20 = -13 ]", "So the expression becomes:\n[ \frac{1}{2} \left| -13 \right| ]", "The absolute value of (-13) is (13):\n[ \frac{1}{2} \ imes 13 = \frac{13}{2} ]", "---", "Final Answer:\n[ \boxed{\frac{13}{2}} ]", "---", "Why This Expression Matters in Math and Real Life\nExpressions like this appear in algebra, physics, economics, and engineering. Absolute values ensure non-negative results, which is useful in measuring differences, distances, or deviations from expected values. The clear simplification steps provided here help prevent errors and build foundational problem-solving skills.", "Tips for Solving Similar Problems:\n1. Multiply or divide first inside parentheses.\n2. Apply signs carefully, especially with negative numbers.\n3. Use absolute value notation to emphasize magnitude.\n4. Break the problem into small steps for accuracy.", "Mastering expressions like this strengthens your algebraic toolkit—ideal for students, educators, or anyone building quantitative reasoning!"]