The Correct Answer and Explanation is:
The expression provided is 6a−36a – 36a−3. To identify equivalent expressions, let’s evaluate each one:
- 6a−3+36a – 3 + 36a−3+3: This simplifies to 6a6a6a, which is not equivalent to 6a−36a – 36a−3. Therefore, this is not an equivalent expression.
- (−3a+4a)−6(-3a + 4a) – 6(−3a+4a)−6: Simplifying −3a+4a-3a + 4a−3a+4a gives aaa, so this becomes a−6a – 6a−6, which is not equivalent to 6a−36a – 36a−3.
- 6a=156a = 156a=15: This equation is incorrect because 6a−3≠156a – 3 \neq 156a−3=15. This is a different equation and not equivalent.
- 6a−3=6a−36a – 3 = 6a – 36a−3=6a−3: This is an identical match with the given expression, so it is the correct equivalent expression.
Thus, the equivalent expression is:
- 6a−3=6a−36a – 3 = 6a – 36a−3=6a−3.
Explanation:
To check for equivalent expressions, we need to see if they simplify to 6a−36a – 36a−3. The expression 6a−36a – 36a−3 has the term 6a6a6a, and the constant −3-3−3. For the other expressions to be equivalent, their simplification should match this same form.
In this case, we find that the only correct match is the identity 6a−3=6a−36a – 3 = 6a – 36a−3=6a−3. The other expressions either involve different constants or algebraic terms that don’t simplify correctly to the target expression. Therefore, only the last option is equivalent to 6a−36a – 36a−3.
