https://file.aiquickdraw.com/mathbot/file/1726722602448ek7mm9ho.jpg

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.

Solve each equation. Then tell whether the equation is conditional, an identity, or a contradiction. 1. 7x - 3(2x - 5) + 5 + 3x = 4x + 20 2. 8x - 4x - (x - 7) + 9x + 6 = 12x - 7

Learn how to solve linear equations like 7x - 3(2x - 5) + 5 + 3x = 4x + 20 and 8x - 4x - (x - 7) + 9x + 6 = 12x - 7. This example illustrates how to identify contradictions in equations and understand when no solutions exist. Suitable for students in Grades 8-10.

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