Combining like terms first
Simplify Grade 9 algebra equations by combining like terms first before isolating variables, reducing multi-step equations to simpler forms for faster, error-free solving.
Key Concepts
Property If there are like terms on one side of an equation, combine them first. Then apply inverse operations and the properties of equality to continue solving the equation.
Examples Solve $6x + 5 2x + 3 = 18$. First, combine like terms: $4x + 8 = 18$. Then solve: $4x = 10$, so $x = 2.5$. In $12 + 5y 2y = 21$, combine the $y$ terms to get $3y + 12 = 21$. Then subtract 12: $3y = 9$. Finally, divide by 3: $y = 3$. For $z + z + 6 + z = 21$, group the $z$'s: $3z + 6 = 21$. Solving gives $3z = 15$, which means $z=5$.
Explanation Before you start solving, tidy up the equation! Grouping and combining all the like terms on one side simplifies the problem into a basic two step equation. It’s like organizing your desk before doing homework—it makes everything clearer and easier to handle. This first step will save you from future headaches and mistakes.
Common Questions
What are like terms and how do you combine them?
Like terms have the same variable raised to the same power. You combine them by adding or subtracting their coefficients. For example, 3x + 5x = 8x, and 7y - 2y = 5y.
Why should you combine like terms before solving an equation?
Combining like terms first reduces the number of terms in the equation, making subsequent steps simpler and less prone to error. An equation like 4x + 3 + 2x - 1 = 20 becomes 6x + 2 = 20 — much easier to solve.
What mistakes do students make when combining like terms?
Common errors include combining terms with different variables (adding 3x and 4y), combining terms with different exponents (adding x² and x), and forgetting to carry the sign when a term is subtracted.