Let's analyze and solve each equation from the image.

The equations are:

(a) $178300 + (x + 340125) = 551925$

(b) $423700 - (x - 60498) = 121156$

Solution for (a)

1. Rewrite the equation: $178300 + x + 340125 = 551925$

2. Combine the known terms on the left side: $518425 + x = 551925$

3. Isolate $x$ by subtracting 518425 from both sides: $x = 551925 - 518425$ $x = 33500$

So, the solution for (a) is $x = 33500$.

Solution for (b)

1. Rewrite the equation: $423700 - x + 60498 = 121156$

2. Combine the known terms on the left side: $484198 - x = 121156$

3. Isolate $x$ by subtracting 121156 from both sides: $-x = 121156 - 484198$ $-x = -363042$

4. Multiply both sides by -1 to solve for $x$: $x = 363042$

So, the solution for (b) is $x = 363042$.

Summary

• For (a): $x = 33500$
• For (b): $x = 363042$

Would you like a detailed step-by-step explanation for any part?

Here are five related questions to deepen your understanding:

1. How can we check our solutions to ensure they are correct?
2. What are the properties of equations that allow us to isolate variables?
3. How would these steps change if we had more variables in each equation?
4. How can we apply similar techniques to inequalities?
5. What methods are there for solving equations with exponents or radicals?

Tip: Always double-check by substituting your solutions back into the original equations to ensure they satisfy the equations.