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Equation solving is a key skill in algebra that involves finding the values of variables that make an equation true. Equations often have an equals sign ( = ), and the goal is to balance both sides by adjusting the unknown variable, often represented by symbols like X . In the original exercise, the unknowns are the missing amounts that need to be calculated.

To solve an equation, we use strategies to isolate the variable on one side of the equation. This can include adding, subtracting, multiplying, or dividing both sides by the same number. By performing the same operation on both sides, we maintain the equation's balance.

• Part (a) is a straightforward addition equation: X = 85,000 + 215,600 , making the solution a simple calculation.
• Part (b) involves subtraction: 93,500 = X + 6,150 . We subtract 6,150 from both sides to isolate X .
• Part (c)'s setup is 42,500 = 11,275 + X . Similarly, subtract 11,275 from both sides to find X .

Understanding equation solving helps students tackle various mathematical problems beyond just algebra.

In algebra, mathematical operations are crucial for manipulating equations and solving for unknown variables. These operations include addition, subtraction, multiplication, and division, and they are the backbone of equation solving.

In this specific problem, only addition and subtraction are needed:

• Addition: When dealing with equations like part (a), you add the numbers together to find the sum. Here, 85,000 + 215,600 gives 300,600 .
• Subtraction: For parts (b) and (c), subtraction helps isolate X . In part (b), subtracting 6,150 from 93,500 yields 87,350 . In part (c), 42,500 - 11,275 results in 31,225 .

These operations are often combined in more complex problems, requiring a sound understanding of their properties and applications in solving equations.

Successful problem solving in algebra often requires following clear, logical steps. This systematic approach ensures accuracy and can make seemingly complex problems manageable.

Here’s a breakdown of the general steps used in this exercise:

• Understand the Problem: Identify what is being asked. Determine which numbers are given and what you are solving for.
• Set Up the Equation: Write the equation based on the problem description. For example, you might have something like X = 85,000 + 215,600 .
• Manipulate the Equation: Use mathematical operations to isolate the variable. This might involve adding or subtracting terms from both sides of the equation.
• Calculate the Solution: Perform the operations needed to solve for X . Double-check each step for accuracy.
• Verify the Solution: Substitute back into the original equation to ensure it holds true.

By consistently applying these steps, students develop a structured approach to problem-solving that can be applied to both simple and more complex algebraic equations.