Question

Which expression is equivalent to the expression quantity negative 6 over 5 times t plus 3 over 16 end quantity minus expression quantity negative 7 over 10 times t plus 9 over 8 end quantity

Answer 1

To simplify the given expression, we distribute the negative sign, combine like terms, and perform arithmetic operations.

Step-by-step explanation:

To simplify the expression:

quantity negative 6 over 5 times t plus 3 over 16 end quantity minus expression quantity negative 7 over 10 times t plus 9 over 8 end quantity

We can distribute the negative sign to both terms inside the first quantity:

negative 6 over 5 times t becomes negative 6t over 5

3 over 16 remains the same

Similarly, we distribute the negative sign to both terms inside the second quantity:

negative 7 over 10 times t becomes negative 7t over 10

9 over 8 remains the same

Now, we can combine like terms by adding or subtracting the fractions with the same denominators:

Combining -6t/5 and -7t/10 gives us -12t/10

Combining 3/16 and 9/8 gives us 6/16

The resulting expression is:

-12t/10 - 6/16

Answer 2

The given expression is:

-(6/5)t + 3/16 - (7/10)t + 9/8

To simplify the expression, we can combine the like terms. The like terms are the terms that have the same variable raised to the same power. Here, the like terms are the terms that involve t:

= -(6/5)t - (7/10)t + 3/16 + 9/8

= -(12/10)t - (7/10)t + 3/16 + 18/16

= -(19/10)t + 21/16

Hence, the equivalent expression is -19/10t + 21/16.