A binary operation × is defined by a × b = ab + a + b for any real numbers a and b. If the identity

Explanation

The inverse of 2 is a number x such that 2 × x equals 0, the identity element. Using the operation definition: 2 times x plus 2 plus x equals 0. This is the equation we need to solve.

Combine like terms: 2x plus x plus 2 equals 0 simplifies to 3x plus 2 equals 0. Subtract 2 from both sides: 3x equals negative 2.

Divide both sides by 3: x equals negative 2 over 3. Verify: 2 times negative two-thirds plus 2 plus negative two-thirds equals negative four-thirds plus two minus two-thirds equals negative four-thirds plus six-thirds minus two-thirds equals 0. Correct.