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State true or false for the following statement: ‘The solution of the equation $4 − 2 (z − 4) 3 = 12 (2 z + 5)$ is $52$ .’

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True

False

answer is A.

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Detailed Solution

The given linear equation is as follows,

4 − 2 (z − 4) 3 = 12 (2 z + 5)

.
We take the LCM of both the denominators and then multiply the LCM on both sides of the equation.
So, multiplying each side of the given equation by 6 and simplifying, we get,

4 (6) − 2 (z − 4) 3 (6) = 12 (2 z + 5) (6) 24 − 4 (z − 4) = 3 (2 z + 5)

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

24 − 4 (z − 4) = 3 (2 z + 5) 24 − 4 (z) − 4 (− 4) = 3 (2 z) + 3 (5) 24 − 4 z + 16 = 6 z + 15 40 − 4 z = 6 z + 15

40 − 4 z − 40 = 6 z + 15 − 40 − 4 z = 6 z − 25 − 10 z = − 25 − 10 z − 10 = − 25 − 10 z = 52

So, the value of the variable z is

52

, which is in accordance with the statement.
Hence, the given statement is true.
So, the correct option is 1.

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