Question

Combine like terms to create an equivalent expression. enter any coefficients as simplified proper or improper fractions or integers. {-2/3a + 5/6a - 1/6} - 3/2a + 6/5a - 6/1

a) -4/5a - 18
b) -4/15a - 1/6
c) -5/6a + 3
d) -2/3a - 29/30

Answer 1

To combine like terms, we add or subtract the coefficients of the same variable. In this question, we combine the terms with 'a' and the constant terms separately and then combine them. The correct equivalent expression is option (b) -4/15a - 1/6.

Step-by-step explanation:

To combine like terms in the given expression, we need to add or subtract the coefficients of the same variable.

First, let's combine the terms with 'a': -2/3a + 5/6a - 3/2a + 6/5a - 6/1a. We can add the coefficients of 'a' together to get -2/3 + 5/6 - 3/2 + 6/5 - 6/1. The common denominator for these fractions is 30, so the expression becomes (-20 + 25 - 45 + 36 - 180)/30, which simplifies to -184/30 or -92/15a.

Next, we combine the constant terms: -1/6 - 0. The result is -1/6.

Lastly, we combine the terms with variables and the constant terms: -92/15a - 1/6. The final equivalent expression is option (b) -4/15a - 1/6.