Bài toán 6: Tìm x thuộc Z để: a. 1 : x là số nguyên b. 1 : (x – 1) là số nguyên c. 2 : x là số nguyên. d. -3 : (x – 2) là một số nguyên e. -5 : (x – 4) là một số nguyên Ê. (x + 8) (x + 7) f. (2x – 9)...

To solve the given problem, we need to find the values of x that satisfy all the given conditions. We can start by analyzing each condition separately and then combine them to find the common solutions. a. 1 : x là số nguyên This means that x must be a divisor of 1, which includes all integers except 0. b. 1 : (x – 1) là số nguyên Similar to part a, this implies that (x - 1) must be a divisor of 1, so (x - 1) can take any integer value. c. 2 : x là số nguyên Here, x must be a divisor of 2, which includes both positive and negative integers. d. -3 : (x – 2) là một số nguyên This indicates that (x - 2) must be a divisor of -3. The divisors of -3 are {-3, -1, 1, 3}, so (x - 2) can take these values accordingly. e. -5 : (x – 4) là một số nguyên Similarly, this implies that (x - 4) must be a divisor of -5. The divisors of -5 are {-5, -1, 1, 5}, so (x - 4) can take these values accordingly. Now let's combine these conditions to find the common solutions: We need to find the intersection of all possible values for x from each condition: - For part a: $x \neq0$ - For part b: $x-1$ can take any integer value. - For part c: $x$ can take any integer value. - For part d: $x-2$ can take values from {-3,-1,1,3}. - For part e: $x-4$ can take values from {-5,-1,1,5}. By considering all these conditions together and finding their intersection: The common solutions for x are [-2,-1,0,1]. Now let's move on to parts Ê and f: Ê. $\frac{(x +8)}{(2-x)} = \frac{(9+x)}{(5-x)}$ f. $\frac{(2-x)(9+x)}{(7+x)(5-x)} = \frac{-(9+2x)}{-(7+x)}$ By solving these equations using the previously found common solutions for x: For Ê: When x = [-2,-1], we get [(6/4),(-7/7)] which simplifies to [3,-1]. For f: When x = [-2,-1], we get [(11/-6),(11/-6)] which simplifies to [-11/6]. Finally moving on to g: g. $\frac{(5+x)(9+x)}{(7+x)(8+x)} = \frac{-(10+13x)}{-(8+x)}$ By solving this equation using the previously found common solutions for x: When x = [-2,-1], we get [(14/15),(-22/7)] which simplifies to [14/15,-22/7]. Therefore combining all the results from each step: The final answer is Solutions: [-2,-1,0,1].