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Mathematics

Statement 1: ax+bcx+d=pq\dfrac{ax + b}{cx + d} = \dfrac{p}{q}.

⇒ q(cx + d) = p(ax + b)

This process is cross-multiplication.

Statement 2: ax + b = c becomes ax = c - b after transposition.

Which of the following options is correct?

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Linear Eqns One Variable

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Answer

Given, ax+bcx+d=pq\dfrac{ax + b}{cx + d} = \dfrac{p}{q}

On cross-multiplication,

⇒ q(ax + b) = p(cx + d)

So, statement 1 is false.

Transposition is a fundamental algebraic technique used to isolate a variable by moving terms from one side of an equation to the other. When a term is transposed, its sign changes;

  • A term added to one side gets subtracted on the other.

  • A term subtracted from one side gets added on the other.

∴ ax + b = c becomes ax = c - b after transposition.

So, statement 2 is true.

∴ Statement 1 is false, and statement 2 is true.

Hence, option 4 is the correct option.

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