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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 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: $2x + 6 = 0$

$

\Rightarrow 2x = - 6 \\

\Rightarrow x = - \dfrac{6}{2} \\

$

Hence $x = ( - 3)$ which is an integer

In option B: $3x - 5 = 0$

$

\Rightarrow 3x = 5 \\

\Rightarrow x = \dfrac{5}{3} \\

$

Hence $x = \dfrac{5}{3}$ which is a fraction

In option C: $5x - 8 = x + 4$

$

\Rightarrow 5x - x = 4 + 8 \\

\Rightarrow 4x = 12 \\

\Rightarrow x = 3 \\

$

Hence $x = 3$ which is an integer

In option D: $4x + 7 = x + 2$

Hence $x = \left( { - \dfrac{5}{3}} \right)$ 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 fraction. They are proper fraction, improper fraction and mixed fraction. Fractions are those terms which have numerator and denominator. For example,$\dfrac{9}{2}$ is a proper fraction, but $\dfrac{8}{3}$ is not.

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