Application of Linear Equations - September 13, 2013
Welcome to today's math adventure! We're diving into the practical side of linear equations: applying them to real-world problems. Get ready to translate word problems into algebraic expressions and solve for those unknowns!
Class Warm-Up
Let's start with a warm-up. Review two homework problems you found challenging. Identify where you got stuck and explain why. For example, consider these example problems:
Example 1:
$$2(x + 6) = -2(x - 4)$$ $$2x + 12 = -2x + 8$$ $$4x + 12 = 8$$ $$4x = -4$$ $$x = -1$$Example 2:
$$\frac{3}{4}(\frac{4}{5}x - 2) = \frac{11}{4}$$ $$20(\frac{12}{20}x - \frac{6}{4}) = \frac{11}{4} * 20$$ $$12x - 30 = 55$$ $$12x = 85$$ $$x = \frac{85}{12}$$Key Concepts: Translating Words to Math
The key to solving application problems is translating the words into mathematical equations. Look for keywords that indicate operations:
- "Sum" or "more than" means addition (+)
- "Difference" or "less than" means subtraction (-)
- "Product" means multiplication (*)
- "Quotient" means division (/)
- "Is" or "equals" means equality (=)
Example: Application Problems
Let's tackle a classic: the Fahrenheit to Celsius conversion.
$$F = \frac{9}{5}C + 32$$If $F = 109.3$, then solving for $C$:
$$109.3 = \frac{9}{5}C + 32$$ $$109.3 - 32 = \frac{9}{5}C$$ $$77.3 = \frac{9}{5}C$$ $$C = \frac{5}{9} * 77.3$$ $$C = -78.5$$Homework Assignment
For homework, complete problems 8-14 on page 37. These problems will give you further practice in applying linear equations. Focus on carefully translating the word problems and showing your work step-by-step.
Remember, practice makes perfect! Don't be afraid to ask questions in class if you get stuck. Good luck, and have fun applying your math skills!