State true or false: The solution of $3 t − 2 4 − 2 t + 3 3 = 23 − t$ is t = 2.

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True

False

answer is A.

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Detailed Solution

The given linear equation is as follows,

3 t − 2 4 − 2 t + 3 3 = 23 − t

.
We first multiply each side of the given equation by 12 and simplify.

3 t − 2 4 (12) − 2 t + 3 3 (12) = 23 − t (12)

Now, we will use the distributive property of multiplication, and simplify the above equation as follows,

3 (3 t − 2) − 4 (2 t + 3) = 8 − 12 t 3 (3 t) + 3 (− 2) − 4 (2 t) − 4 (3) = 8 − 12 t 9 t − 6 − 8 t − 12 = 8 − 12 t t − 18 = 8 − 12 t

t − 18 + 12 t = 8 − 12 t + 12 t 13 t − 18 = 8

13 t − 18 + 18 = 8 + 18 13 t = 26 13 t 13 = 2613 t = 2

So, the value of the variable t is 2, which is in accordance with the statement.
Hence, the given statement is true.
So, the correct option is 1.

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