Question

Решите |x+7 |= 14|x - 2|= 6|4x-8| =12|7x-35|=7|8x-16|= 24|x-4|=2x+5​

Answer 1

Ответ:

1) х=14-7

х=7

ответ: х=7

2) х=6+2

х=8

ответ: х=7

Answer 2

We can solve this equation by breaking it down into several cases based on the different values of x that make each absolute value equal to its respective expression.

Case 1: |x + 7| = 14 If x + 7 is positive, then we have x + 7 = 14, which gives us x = 7. If x + 7 is negative, then we have -(x + 7) = 14, which gives us x = -21. Therefore, the solutions for this case are x = -21 and x = 7.

Case 2: |x - 2| = 6 If x - 2 is positive, then we have x - 2 = 6, which gives us x = 8. If x - 2 is negative, then we have -(x - 2) = 6, which gives us x = -4. Therefore, the solutions for this case are x = -4 and x = 8.

Case 3: |4x - 8| = 6 If 4x - 8 is positive, then we have 4x - 8 = 6, which gives us x = 7/2. If 4x - 8 is negative, then we have -(4x - 8) = 6, which gives us x = -1/2. Therefore, the solutions for this case are x = -1/2 and x = 7/2.

Case 4: |7x - 35| = 12 If 7x - 35 is positive, then we have 7x - 35 = 12, which gives us x = 47/7. If 7x - 35 is negative, then we have -(7x - 35) = 12, which gives us x = 23/7. Therefore, the solutions for this case are x = 23/7 and x = 47/7.

Case 5: |8x - 16| = 7 If 8x - 16 is positive, then we have 8x - 16 = 7, which gives us x = 23/8. If 8x - 16 is negative, then we have -(8x - 16) = 7, which gives us x = 9/8. Therefore, the solutions for this case are x = 9/8 and x = 23/8.

Case 6: |x - 4| = (2x + 5)/12 If x - 4 is positive, then we have x - 4 = (2x + 5)/12, which gives us x = 64/5. If x - 4 is negative, then we have -(x - 4) = (2x + 5)/12, which gives us x = -7/5. Therefore, the solutions for this case are x = -7/5 and x = 64/5.

Therefore, the solutions to the given equation are x = -21, -4, -1/2, 7/2, 9/8, 23/7, 23/8, and 64/5.