已知关于x的方程1/2(10x-3a)=2(2+3x)的解为质数,求a

X=-(8+3a)/2

X为质数......

解出x 然后利用质数条件 判断

(10x-3a)/2=2(2+3x)
等式两边同乘2：10x-3a=8+12x
求得：x=(-3a-8)/2<0
求得：a>-8/3

X=-(8+3a)/2大于等于2 X为质数 a 小于等于-4

First we use algebra to manipulate the equation as:
0.5*(10x - 3a) = 2(2 + 3x) => -2x = 8 + 3a => x = -4 - (3a)/2.

Now we know that x is a prime number (let us assume a prime number is always greater than 2) then -4 - (3a)/2 > 2 => a > -4.

And a = (-2x -8)/3;

Further, a prime number is one element of the set {2,3,5,7,11 ...}.
so:
when x = 2, a = -4;
when x = 3, a = -14/3;
when x = 5, a = -6;
...

Now the question is: can we use one analytical expression to express a prime number as a function of one or more parameters? Well probably the answer is No. So we have to PROVE BY INDUCTION, which leads the answer to be a belongs to {-4, -14/3, -6, ...}, so it is NOT INCOR