56.7k views
2 votes
Which expression is equivalent to the expression quantity negative 7 over 6 times t plus 4 over 9 end quantity minus expression quantity negative 5 over 12 times t plus 2 over 3 end quantity?

negative 12 over 18 times t plus 6 over 12
negative 9 over 12 times t minus 2 over 9
12 over 18 times t plus negative 6 over 12
2 over 12 times t plus 2 over 6

1 Answer

3 votes

Final answer:

To simplify the expression, combine like terms and find a common denominator for the fractions. The expression is equivalent to 8t/9 + 16/9.

Step-by-step explanation:

To simplify the expression, we need to combine like terms. First, let's multiply:

-7/6 * t = -7t/6

-5/12 * t = -5t/12

Now, let's find a common denominator for the fractions:

6 and 12 have a common denominator of 12. This means we need to rewrite 4/9 as 4/9 * 12/12 = 48/108.

Similarly, we need to rewrite 2/3 as 2/3 * 6/6 = 12/18.

Now, let's combine the terms:

(-7t/6 + 48/108) - (-5t/12 + 12/18)

= -7t/6 + 48/108 + 5t/12 - 12/18

Now, let's simplify the fractions:

= -7t/6 + 48/108 + 5t/12 - 12/18

= (-14t + 288 + 30t - 96)/108

= (16t + 192)/108

= 8t/9 + 16/9

Therefore, the expression is equivalent to 8t/9 + 16/9.

User Oppih
by
9.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories