Let's go over these equations one by one, breaking them down in a way that's easy to understand!

1. 3y + 1 ≤ y This equation means: "Three times a number (y) plus 1 is less than or equal to just the number (y)." To solve this, we can move things around to isolate y and find the value.

2. x² + 4x + 6 This is a quadratic equation! It's in the form of x² (x squared), plus 4 times x, plus 6. We can try factoring or using the quadratic formula to find the value of x.

3. (x - 1)/3 < 12 This means "x minus 1, divided by 3, is less than 12." We can solve this by multiplying both sides by 3 and then isolating x.

4. 4y + 3 = 18 + y This is a linear equation that says "Four times a number (y) plus 3 equals 18 plus that same number (y)." To solve, we need to get y by itself.

5. w/5 + z = 16 This means "w divided by 5, plus z, equals 16." To solve this, we can subtract z from both sides and then multiply both sides by 5.

6. 14/(2a) + a + 1 This is a bit more complicated. It says "14 divided by 2 times a, plus a, plus 1." To solve, we can first simplify the fraction and then combine like terms.

Would you like me to walk you through the step-by-step process for any of these equations?

Here are some follow-up questions that may help you dive deeper:

1. How do we move terms around in equations to isolate variables?
2. What is the quadratic formula, and how do we use it to solve equations like the second one?
3. How do we solve inequalities like the third equation?
4. What does it mean for an equation to be "linear" like the fourth one?
5. Can you explain the process of solving equations with fractions, like the last one?

Tip: Always check if you can simplify the equation first, such as combining like terms, before starting to solve!