Let's focus on solving problems 3 and 4, which are visible in the image.

Problem 3:

$\frac{1}{2}(2x - 6) + 5 = 2x + 9 - x$

Steps to solve:

1. Expand the expression on the left-hand side.
2. Combine like terms on both sides.
3. Solve for $x$.

Problem 4:

$2(x + 1) + 3(2x + 1) = -7$

Steps to solve:

1. Distribute the constants in the expressions on the left-hand side.
2. Combine like terms.
3. Solve for $x$.

I'll now solve these equations.### Solutions:

• Problem 3: The equation $\frac{1}{2}(2x - 6) + 5 = 2x + 9 - x$ has no solution. This implies that the equation is either contradictory or simplifies to something false like $1 = 0$.

• Problem 4: The equation $2(x + 1) + 3(2x + 1) = -7$ has a solution: $x = -\frac{3}{2}$

Do you want further details on these solutions, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. How can you determine if an equation has no solution by analyzing it?
2. What happens to the solution set of an equation if you get a statement like $0 = 0$?
3. How do you solve systems of equations where one equation has no solution?
4. Can equations with no solutions occur in real-world problems?
5. How do equations with fractions change the steps you need to follow?

Tip: Always check for contradictions when solving equations to identify if there's no solution!