Question

If \[8x - 3 = - 25 + 17x\] , then ‘x’ is
A.A fraction
B.An integers
C.A rational number
D.Cannot be solved.

Answer 1

Hint: Given a problem is a simple equation with only one unknown value or only one variable. We can easily solve this. To answer this question we need to know the definition of fraction, integer and a rational number. After simplifying the problem we get the value of ‘x’. By using the definition we can answer this easily

Complete step-by-step answer:
Given,
 \[8x - 3 = - 25 + 17x\]
Simply rearranging the terms ‘x’ in one side of the equation and constants on the other side of the equation. We get,
 \[ \Rightarrow 8x - 17x = - 25 + 3\]
Now taking ‘x’ as a common term in the left hand side of the equation,
 \[ \Rightarrow (8 - 17)x = - 25 + 3\]
Subtracting we have,
 \[ \Rightarrow - 9x = - 22\]
Multiply by negative sign on both side we get,
 \[ \Rightarrow 9x = 22\]
Divided by 9 on both sides we have,
 \[ \Rightarrow x = \dfrac{{22}}{9}\] .
Now we have the value of ‘x’.
 \[ \bullet \] Fractions represent equal parts of a whole or a collection. It is represented by \[\dfrac{a}{b}\] , a is called the numerate term and b is called the denominator term. ‘a’ and ‘b’ are natural numbers.
 \[ \bullet \] An integer is a number which is not a fraction (no decimal).
 \[ \bullet \] The rational numbers are represented by \[\dfrac{a}{b}\] . ‘a’ and ‘b’ are integers.
In \[x = \dfrac{{22}}{9}\] both 22 and 9 are natural numbers.
Hence ‘x’ is a fraction.
But, we know that all fractions are rational numbers.
So, the correct answer is “Option A and C”.

Note: We know that not all rational are fractions. Only the rational numbers where both ‘a’ and ‘b’ have positive integers are fractions. If we have the value of ‘x’ as \[x = \dfrac{{ - 22}}{9}\] . Then ‘x’ is a rational number but not a fraction. This is because of negative signs, it became integer. In fraction both numbers are natural numbers.