I can now see the two equations that you would like solved:

Equation 5:
$7x - 3(2x - 5) + 5 + 3x = 4x + 20$

Equation 6:
$8x - 4x - (x - 7) + 9x + 6 = 12x - 7$

Let me solve both and determine whether they are conditional, an identity, or a contradiction.

Starting with equation 5:
$7x - 3(2x - 5) + 5 + 3x = 4x + 20$ I'll simplify and solve for $x$.For equation 5, there is no solution, which means this is a contradiction. The equation leads to an inconsistency, so there is no value of $x$ that satisfies it.

Next, I will solve Equation 6: $8x - 4x - (x - 7) + 9x + 6 = 12x - 7$ Let me simplify and solve it.For equation 6, there is also no solution, which makes it another contradiction. This means there is no value of $x$ that will satisfy this equation.

Would you like further details or explanations on how these conclusions were reached?

Here are some related questions to explore further:

1. How can you identify a contradiction in a linear equation?
2. What distinguishes an identity from a conditional equation?
3. Could both sides of an equation have no variable but still be a contradiction?
4. How do you check if a solution to an equation is conditional?
5. What types of equations lead to an infinite number of solutions?

Tip: Always simplify equations step by step, combining like terms and removing parentheses early to avoid errors.