Question

Which equation has only one solution?

1) |5x + 10| - 10 = 0
2) -2|x – 5| = 2
3) |–6x + 3| / 10 = 10
4) |–6 – 2x| - 8 = 0

Answer 1

The equation |5x + 10| - 10 = 0 has only one solution: x = 0.

Step-by-step explanation:

To determine which equation has only one solution, we need to solve each equation and see how many solutions we get.

1) The equation |5x + 10| - 10 = 0 can be rewritten as 5x + 10 - 10 = 0 or 5x + 10 + 10 = 0. Both equations simplify to 5x = 0, which gives us one solution: x = 0.

2) The equation -2|x - 5| = 2 can be rewritten as -2(x - 5) = 2 or -2(x - 5) = -2. Both equations simplify to -2x + 10 = 2, which gives us one solution: x = 4.

3) The equation |–6x + 3| / 10 = 10 can be rewritten as –6x + 3 = 100 or –6x + 3 = -100. The first equation simplifies to -6x = 97, which gives us one solution: x = -97 / 6. The second equation simplifies to -6x = -103, which gives us one solution: x = 103 / 6.