To determine which expression is equivalent to a given expression, we need to simplify or manipulate the original expression to find a matching equivalent form.
For example, let's consider the expression: 3 ( x + 2 ) − 4 .
Step 1: Distribute the 3 into the terms inside the parentheses:
3 ( x + 2 ) = 3 x + 6
Step 2: Substitute this result back into the expression:
3 x + 6 − 4
Step 3: Combine like terms:
3 x + ( 6 − 4 ) = 3 x + 2
The expression 3 x + 2 is equivalent to the original expression 3 ( x + 2 ) − 4 .
When simplifying expressions, make sure to:
Apply the distributive property correctly.
Combine like terms to simplify the expression.
This process is essential for recognizing and rewriting equivalent expressions in algebra.