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**Hint:**Firstly solve all the four equations given in the options one-by-one, to find the value of x. Then check whether x is a fraction or an integer.

**Complete step-by-step answer:**Let us proceed with solving all the four equations given in the option one-by-one.

In option A: 2x+6=0 hence x= (−3) which is an integer

In option B: 3x-5=0 hence x = $\dfrac{5}{3}$ which is a fraction

In option C: 5x-8=x+4 hence x =3 which is an integer

In option D: 4x+7=x+2 hence x =($ - \dfrac{5}{3}$ ) which is neither a proper fraction, nor an integer.

**Hence option (D) is correct, i.e. the solution of the equation 4x+7=x+2 is neither a fraction nor an integer.**

**Note:**An integer is a whole number that can be positive, negative, or zero.

In Maths, there are three major types of fractions. They are proper fractions, improper fractions and mixed fractions. Fractions are those terms which have numerator and denominator.

Note that, in a proper fraction, the value of the numerator is always less than the value of the denominator. For example, $\dfrac{1}{3}$is a proper fraction, but $\dfrac{7}{3}$ is not.

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