Question

300. Решите уравнение. 1) 7|x| — 6|x| = 1; 2) 2 |x| +3|x| = 8; 3) [-х] + 4[-х] = 9; 4) 5[-х] — 2|-x| = 18; 5) [2x] + 3[2x| = 2,4; 6) 4 [3х] + 5 [3x] = 8, 1,​

Answer 1

Ответ:

1)x1=-1,x2=1; 2)x1=-4,x2=2; 3)x=94;4)x=-6; 5)2x+3;6)dxdy =-xy+5 , став❤и бал

Answer 2

1) 7|x| - 6|x| = 1

To solve this equation, we need to consider two cases:

Case 1: x ≥ 0 7x - 6x = 1 x = 1

Case 2: x < 0 7(-x) - 6(-x) = 1 -x = 1 x = -1

Therefore, the solutions to the equation are x = 1 and x = -1.

2) 2|x| + 3|x| = 8

Again, we need to consider two cases:

Case 1: x ≥ 0 2x + 3x = 8 5x = 8 x = 8/5

Case 2: x < 0 2(-x) + 3(-x) = 8 -2x - 3x = 8 -5x = 8 x = -8/5

So the solutions to this equation are x = 8/5 and x = -8/5.

3) [-x] + 4[-x] = 9

This equation can be simplified to: -1x + 4(-1x) = 9 -5x = 9 x = -9/5

Therefore, the solution to this equation is x = -9/5.

4) 5[-x] - 2|-x| = 18

We need to consider two cases:

Case 1: x ≥ 0 5(-x) - 2(-x) = 18 -5x + 2x = 18 -3x = 18 x = -6

Case 2: x < 0 5x - 2(-x) = 18 5x + 2x = 18 7x = 18 x = 18/7

The solutions to this equation are x = -6 and x = 18/7.

5) [2x] + 3[2x] = 2.4

Simplifying this equation: 2(2x) + 3(2x) = 2.4 4x + 6x = 2.4 10x = 2.4 x = 2.4/10 x = 0.24

Therefore, the solution to this equation is x = 0.24.

6) 4 +[3x] + 5 + [3x] = 8 + 1

Simplifying this equation: 4 + 6x + 5 + 6x = 9 12x + 9 = 9 12x = 0 x = 0

Hence, the solution to this equation is x = 0.