Question

1) |2x-3|+|x-3|-|4x-1|=0 2) x^-|x|=6 3) |2x-5|=2-x

Answer 1

3456 - 456 y 15 = 7 x всё просто 

Answer 2

Let's solve each equation step by step:

1. |2x-3| + |x-3| - |4x-1| = 0

We'll consider different cases based on the sign of the expressions inside the absolute value bars.

Case 1: (2x-3) ≥ 0, (x-3) ≥ 0, (4x-1) ≥ 0 In this case, the equation simplifies to: (2x-3) + (x-3) - (4x-1) = 0 2x - 3 + x - 3 - 4x + 1 = 0 -1x - 5 = 0 x = -5

Case 2: (2x-3) ≥ 0, (x-3) < 0, (4x-1) ≥ 0 In this case, the equation simplifies to: (2x-3) - (x-3) - (4x-1) = 0 2x - 3 - x + 3 - 4x + 1 = 0 -3x + 1 = 0 3x = 1 x = 1/3

Case 3: (2x-3) < 0, (x-3) ≥ 0, (4x-1) ≥ 0 In this case, the equation simplifies to: -(2x-3) + (x-3) - (4x-1) = 0 -2x + 3 + x - 3 - 4x + 1 = 0 -5x + 1 = 0 5x = 1 x = 1/5

Case 4: (2x-3) < 0, (x-3) < 0, (4x-1) ≥ 0 In this case, the equation simplifies to: -(2x-3) - (x-3) - (4x-1) = 0 -2x + 3 - x + 3 - 4x + 1 = 0 -7x + 7 = 0 7x = 7 x = 1

Case 5: (2x-3) < 0, (x-3) < 0, (4x-1) < 0 In this case, the equation simplifies to: -(2x-3) - (x-3) + (4x-1) = 0 -2x + 3 - x + 3 + 4x - 1 = 0 x + 5 = 0 x = -5

So, the solutions to the equation are x = -5, x = 1/3, x = 1/5.

2. x^(-|x|) = 6

Since the exponent is negative, we need to consider different cases based on the sign of x.

Case 1: x > 0 In this case, the equation simplifies to: x^(-x) = 6

Case 2: x < 0 In this case, the equation simplifies to: x^(x) = 6

Unfortunately, these equations do not have simple algebraic solutions. You can use numerical methods or approximation techniques to find the values of x that satisfy the equations.

3. |2x-5| = 2 - x

We'll consider different cases based on the sign of the expression inside the absolute value bars.

Case 1: (