Part 1. The graph is represented by 3 <= x <= 5. Since each inequality has 1 on the right hand side, what can you do to 3 <= x <= 5 to get a 1 on the far right? Subtract 4 from each part of the inequality:

3 - 4 <= x - 4 <= 5 - 4, which means that -1 < x - 4 < 1, which means that |x - 4| < 1.

Part 2. 2 * | 3x - 1 | + 2 = 10. Divide thru by the common factor of 2, getting |3x - 1| + 1 = 5. Now get the absolute value by itself, subtracting 1 on both sides of the inequality,resulting in |3x-1| = 4. This can happen in two ways: a) if 3x-1 = 4 or b) 3x-1 = -4. a) implies that 3x = 5, so that x = 5/3. b) implies that 3x = -3, so that x = -1. So, the solutions are x = 5./3 and x = -1.

Part 3. 13x - 4 - 9x + 20 = 0 impliies that 13x - 9x - 4 + 20 = 0, which implies that 4x + 16 = 0, which means that 4x = -16, so that x = -4.