Question

The solution of which of the following equations is neither a fraction nor an integer?

• A. $2x+6=0$
• B. $3x–5=0$
• C. $5x–8=x+4$
• D. $4x+7=x+2$

Answer 1

The correct option is D

$4x+7=x+2$

Option (a)

$\begin{array}{rcl}2x+6& =& 0\\ 2x& =& -6\\ x& =& -6/2\\ x& =& -3\end{array}$

So, it is an Integer.

Option (b)

$$\begin{gathered} 3x–5=0 \\ 3x=5 \\ x=\frac{5}{3} \end{gathered}$$()

So, it is a Fraction.

Option (c)

$\begin{array}{rcl}5x–8& =& x+4\\ 5x& =& x+4+8\\ 5x& =& x+12\\ 5x–x& =& 12\\ 4x& =& 12\\ x& =& 12/4\\ x& =& 3\end{array}$

So, it is an Integer.

Option (d)

$\begin{array}{rcl}4x+7& =& x+2\\ 4x& =& x+2–7\\ 4x& =& x–5\\ 4x–x& =& -5\\ 3x& =& -5\\ x& =& -5/3\end{array}$

Hence, It is neither integer nor fraction because in case of fraction both numerator and denominator has to a whole number.