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Maths-

General

Easy

Question

$fraction numerator 4 x plus b over denominator 2 end fraction equals 2 x plus 8$
In the given equation, $b$ is a constant. If the equation has infinitely many solutions, what is the value of $b$ ?

2
4
8
16

The correct answer is: 16

If a linear equation has infinitely many solutions, LHS = RHS
Step-by-step solution:-
Simplifying the given equation, we get-
$fraction numerator 4 x plus b over denominator 2 end fraction equals 2 x plus 8$
∴ 4x + b = 2 (2x + 8) ------------- (Multiplying both the sides with 2)
∴ 4x + b = 4x +16 ------------- (equation i)
In the adjacent table, we substitute the values of x & y in equation i above and check whether LHS = RHS.

Final Answer:-
Option D i.e. 16 is the correct Option.
Note:-
Alternatively, we can apply Identity principle i.e. When the equation is simplified, the coefficient of x on LHS and RHS should be equal and the constants on LHS & RHS should be equal
∴ by comparing the constants of LHS and RHS, we get-
b = 16

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