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What is the value of t in $t - (2 t + 5) - 5 (1 - 2 t) = 2 (3 + 4 t) - 3 (t - 4)$ ?

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answer is A.

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Detailed Solution

Given,

t - (2 t + 5) - 5 (1 - 2 t) = 2 (3 + 4 t) - 3 (t - 4)

.
Solve the equation for x.

t - (2 t + 5) - 5 (1 - 2 t) = 2 (3 + 4 t) - 3 (t - 4)

t - 2 t - 5 - 5 + 10 t = 6 + 8 t - 3 t + 12

9 t - 10 = 5 t + 18

9 t - 5 t = 10 + 18

4t = 28
t = 7
Check whether the solution is correct or not by substitution method.

LHS = t - (2 t + 5) - 5 (1 - 2 t)

= 7 - (2 (7) + 5) - 5 (1 - 2 (5))

= 53

RHS = 2 (3 + 4 t) - 3 (t - 4)

= 2 (3 + 4 (7)) - 3 (7 - 4)

= 53

LHS = RHS
So, the value of t is 7.
Hence, option 1 is correct.

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