Question

Difference of 10^25-7 and 10^24+x is divisible by 3 .Find value of x

Answer 1

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Answer 2

Value of x can be (3n + 2), with n ϵ integers.

Solution:

To derive the value of x, first need to check whether the equation is divisible by 3.

First let us simplify the equation in simpler form

$\begin{array}{l}{=10^{25}-7-10^{24}-x} \\ \\{=10^{24}(10-1)-7-x}\end{array}$

After simplifying, we get $=9 \times 10^{24}-(7+x)$

Now what will the value if the above equation is divisible by 3 let us check

$\frac{9 \times 10^{24}-(7+x)}{3}=\frac{9 \times 10^{24}}{3}-\frac{7}{3}+\frac{x}{3}$

Now for $\frac{9 \times 10^{24}}{3}$ we can see that it is divisible by 3 giving the value of $3 \times 10^{24}$

Whereas for $\frac{7}{3}-\frac{x}{3}$  or we can write it as – (7 + x) form that are divisible by 3.

x > 0 , x = 3n +2  i.e., x = 2,5,8

x < 0 , x = 3n +2  i.e., x = -1,-4,-7

Combining two variants into one solution,

Therefore, value of x can be (3n + 2), with n ϵ integers.