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Mathematics

Assertion (A) : (2x + 5)2 - (2x - 5)2 = 40 is a linear equation in terms of one variable.

Reason (R) : An equation in which the greatest exponent of the variable after simplification is one is called a linear equation.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Linear Eqns One Variable

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Answer

An equation in which the greatest exponent of the variable after simplification is one is called a linear equation.

This definition aligns with the standard definition of a linear equation. A linear equation in one variable is of the form ax + b = 0, where a ≠ 0 and the highest power of x is 1.

So, reason (R) is true.

Given,

⇒ (2x + 5)2 - (2x - 5)2 = 40

⇒ 4x2 + 25 + 20x - (4x2 + 25 - 20x) = 40

⇒ 4x2 + 25 + 20x - 4x2 - 25 + 20x = 40

⇒ 40x = 40

⇒ 40x - 40 = 0

The above equation is in the form ax + b = 0, where a = 40, b = -40 and the highest power of x is 1.

So, assertion (A) is true.

∴ Both A and R are correct, and R is the correct explanation for A.

Hence, option 1 is the correct option.

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