Question

Which expression is equivalent to the expression quantity negative 7 over 5 times t plus 2 over 9 end quantity minus expression quantity negative 5 over 15 times t plus 4 over 3 end quantity?

negative 16 over 15 times t minus 10 over 9
negative 16 over 15 times t plus 10 over 9
2 over 5 times t plus 2 over 15
16 over 15 times t plus negative 14 over 15

Answer 1

The equivalent expression to the given original expression is negative 16 over 15 times t minus 10 over 9, obtained by simplifying and combining like terms. Therefore correct option is A

Step-by-step explanation:

To determine which expression is equivalent to the expression given, let's simplify the original expression step-by-step. The original expression is:

(-7/5)t + 2/9 - ((-5/15)t + 4/3)

First, simplify the terms inside the parentheses:

(-7/5)t + 2/9 - (-1/3)t - 4/3, since -5/15 reduces to -1/3.

Now, combine like terms t and constants separately:

((-7/5) + (1/3))t + (2/9 - 4/3)

Find a common denominator for each set of fractions:

((-21/15) + (5/15))t + (2/9 - 12/9)

Combine the fractions:

(-16/15)t - (10/9)

This is the simplified form of the original expression. So, the equivalent expression is negative 16 over 15 times t minus 10 over 9.