Combine Like Terms First
Combining like terms first in Grade 8 Saxon Math Course 3 is an algebraic simplification strategy where students identify and collect terms with the same variable and exponent before performing other operations. Simplifying an expression by combining like terms reduces complexity and makes subsequent solving steps more manageable. This is a foundational skill for all algebraic manipulation.
Key Concepts
Property When a variable appears more than once in an equation, you must first combine all like terms to simplify the equation before you begin isolating the variable.
Examples In $3x + 4 x = 28$, combine $3x$ and $ x$ to get $2x + 4 = 28$, which simplifies to $x=12$. In $4x + 10 + x = 100$, combine $4x$ and $x$ to get $5x + 10 = 100$, which simplifies to $x=18$. In $7x 12 x = 24$, combine $7x$ and $ x$ to get $6x 12 = 24$, which simplifies to $x=6$.
Explanation Your equation is like a messy room! Before you can find your lost variable 'x', you need to tidy up by grouping all the 'x' terms together and all the plain numbers together. A clean equation makes finding the solution so much easier!
Common Questions
What does it mean to combine like terms?
Combining like terms means adding or subtracting terms that have the same variable raised to the same power. For example, 3x + 5x = 8x because both terms have the variable x.
What are like terms in algebra?
Like terms have the same variable(s) with the same exponent(s). For example, 4x and -2x are like terms, but 4x and 4x squared are not.
Why should you combine like terms before solving an equation?
Combining like terms first simplifies the equation, reducing the number of terms and making it easier to apply inverse operations to isolate the variable.
Can you combine a constant with a variable term?
No. Constants (numbers without variables) and variable terms are not like terms. For example, 5 and 3x cannot be combined.
How does Saxon Math Course 3 teach combining like terms?
Saxon Math Course 3 introduces combining like terms as a key simplification step in multi-term equations, requiring students to simplify both sides before solving.