Question

843. 1) |x-1,5 = 4; 2) |3 - x = 5; 3) |2x - 3|= 0; 4) |6 – 5x| = 0; 5) |x +1| + 5 = 3; 6) |x +5-2= 7.​

Answer 1

Ответ:

x = -2.5, 5.5, -2, 8, 3/2, 6/5, -3, -4 или 4.

Пошаговое объяснение:

|x-1,5|=4 означает x = -2.5 или x = 5.5

|3-x|=5 означает x = -2 или x = 8

|2x-3|=0 означает 2x-3 = 0 и x = 3/2

|6-5x|=0 означает 6-5x = 0 и x = 6/5

|x+1|+5 = 3 означает |x+1| = -2 и x = -3

|x+5-2|=7 означает |x+3|=7 и x = -4 или x = 4

Answer 2

To solve these absolute value equations, you need to isolate the absolute value expression on one side of the equation and then consider two cases: one where the expression inside the absolute value is positive and one where it's negative. Here are the solutions for each of the equations:

1. |x - 1.5| = 4: a) x - 1.5 = 4 x = 4 + 1.5 x = 5.5

   b) -(x - 1.5) = 4 -x + 1.5 = 4 -x = 4 - 1.5 -x = 2.5 x = -2.5

2. |3 - x| = 5: a) 3 - x = 5 -x = 5 - 3 -x = 2 x = -2

   b) -(3 - x) = 5 -3 + x = 5 x = 5 + 3 x = 8

3. |2x - 3| = 0: a) 2x - 3 = 0 2x = 3 x = 3/2 x = 1.5

   b) -(2x - 3) = 0 -2x + 3 = 0 -2x = -3 x = (-3)/(-2) x = 3/2 x = 1.5

4. |6 - 5x| = 0: a) 6 - 5x = 0 -5x = -6 x = (-6)/(-5) x = 6/5 x = 1.2

   b) -(6 - 5x) = 0 -6 + 5x = 0 5x = 6 x = 6/5 x = 1.2

5. |x + 1| + 5 = 3: a) |x + 1| = 3 - 5 |x + 1| = -2 There are no real solutions for this case because the absolute value of a real number is always non-negative.

   b) -(x + 1) + 5 = 3 -x - 1 + 5 = 3 -x + 4 = 3 -x = 3 - 4 -x = -1 x = 1

6. |x + 5 - 2| = 7: a) |x + 3| = 7 x + 3 = 7 x = 7 - 3 x = 4

   b) -(x + 3) = 7 -x - 3 = 7 -x = 7 + 3 -x = 10 x = -10

So, the solutions for each equation are as follows:

1. x = 5.5 and x = -2.5
2. x = -2 and x = 8
3. x = 1.5
4. x = 1.2
5. x = 1 (only one solution)
6. x = 4 and x = -10