1) |x+7x-4| = |8x-4| = 4 Solving this equation, we get: 8x-4 = 4 or 8x-4 = -4 8x = 8 or 8x = 0 x = 1 or x = 0
2) 5x-8|x|+3 = 0 This equation does not have real solutions.
3) x|x|+6x-5 = 0 We can rewrite this equation as: |x^2| + 6x - 5 = 0 Using the fact that |x^2| = x^2, we get: x^2 + 6x - 5 = 0 Solving this quadratic equation, we get: x^2 + 6x - 5 = (x+1)(x+5) = 0 Therefore, x = -1 or x = -5
So the solutions to the equations are x = 1, x = 0, x = -1, and x = -5.
1) |x+7x-4| = |8x-4| = 4
Solving this equation, we get:
8x-4 = 4 or 8x-4 = -4
8x = 8 or 8x = 0
x = 1 or x = 0
2) 5x-8|x|+3 = 0
This equation does not have real solutions.
3) x|x|+6x-5 = 0
We can rewrite this equation as: |x^2| + 6x - 5 = 0
Using the fact that |x^2| = x^2, we get:
x^2 + 6x - 5 = 0
Solving this quadratic equation, we get:
x^2 + 6x - 5 = (x+1)(x+5) = 0
Therefore, x = -1 or x = -5
So the solutions to the equations are x = 1, x = 0, x = -1, and x = -5.