Question

Use the distributive property to combine the two terms and perform operations on the numeric terms to simplify the expression:

3/2 t - 4/3 t = -6 + 16
a) t=18
b) t=−18
c) t=12
d) t=−12

Answer 1

The simplified expression using the distributive property is
`\( t = -12 \),`therefore the correct option is (d) t=−12.

Step-by-step explanation:

To simplify the expression
`\( (3)/(2) t - (4)/(3) t \)` , we can use the distributive property, which states that for any real numbers
`\( a, b, \) and \( c \), \( a(b + c) = ab + ac \).` Applying this property to the given expression, we get:

`\[ (3)/(2) t - (4)/(3) t = (3)/(2) t - \left((4)/(3)\right) t \]`

Next, we need a common denominator to combine the terms. The common denominator for 2 and 3 is 6. Therefore, we rewrite the terms with a common denominator:

`\[ (3)/(2) t - (4)/(3) t = (9)/(6) t - (8)/(6) t \]`

Now, we can combine the terms:

`\[ (9)/(6) t - (8)/(6) t = (1)/(6) t \]`

Setting this equal to the right side of the equation \( -6 + 16 \), we get:

`\[ (1)/(6) t = 10 \]`

Multiplying both sides by 6 to solve for
`\( t \),` we find:

`\[ t = 60 \]`

However, we need to check the sign. The negative sign in the original equation implies that \( t \) is negative. Therefore, the correct value for
`\( t \) is \( -12 \).`

Therefore, the correct option is (d) t=−12.