Mastering Linear Equations and Word Problems

📋 Course Outline

1. Linear equations with fractions
2. Solving linear equations with variables
3. Harder challenge linear equation problems
4. Word problems: perimeter and dimensions
5. Word problems: cost, tickets, and integers

📖 1. Linear equations with fractions

🔑 Key Concepts & Definitions

• Linear equation : A linear equation is an equation where the variable appears only to the first power and not inside products of variables.
• Common denominator : A common denominator is a shared multiple used to rewrite fractions so they can be added or subtracted easily.
• Distributive property : The distributive property lets you multiply a number across terms inside parentheses.

📝 Essential Points

• Clear fractions by multiplying both sides by the least common denominator of all fractional coefficients.
• When fractions include expressions like (x-10) or (2x+5), distribute before combining like terms.
• After clearing denominators, collect x-terms on one side and constants on the other side.
• Solve by isolating x, then check by substituting into the original fractional equation.

💡 Memory Hook

Fractions first: clear denominators, then collect x, then isolate x.

📖 2. Solving linear equations with variables

🔑 Key Concepts & Definitions