Problem 59 - Basic College Mathematics

Question

Solve. $$ 8797=y+2299 $$

Step-by-Step Solution

Answer

y = 6498.

Step 1 - Identify the equation

The given equation is 8797 = y + 2299.

Step 2 - Isolate the variable

Subtract 2299 from both sides of the equation to isolate the variable y. 8797 - 2299 = y + 2299 - 2299.

Step 3 - Simplify the equation

Perform the subtraction on the left side: 8797 - 2299 = 6498. So, y = 6498.

Key Concepts

solving equations

Solving equations is a fundamental skill in mathematics. The main goal is to find the value of the variable that makes the equation true. For instance, in our original exercise, the equation is given as 8797 = y + 2299. The task is to determine the value of y that satisfies this equation. There are several steps involved, including identifying and rewriting the equation, isolating the variable, and performing basic arithmetic operations. It's essential to carefully follow each step to arrive at the correct solution.

variable isolation

Variable isolation means getting the variable alone on one side of the equation. In the original exercise, our goal is to isolate y in the equation 8797 = y + 2299.
To achieve this, we need to 'get rid' of the 2299 from the right side of the equation. This can be done by performing the inverse operation. Since 2299 is being added to y, we subtract 2299 from both sides of the equation to cancel it out. This gives us:
$$8797 - 2299 = y + 2299 - 2299$$

Once we simplify this, we will have y isolated on one side of the equation and a numerical value on the other side.

basic arithmetic

Basic arithmetic involves performing simple operations like addition, subtraction, multiplication, and division. In the context of the given problem, subtraction is primarily used. When we subtract 2299 from both sides:
$$8797 - 2299 = 6498$$
This means y equals 6498. Performing such operations accurately is crucial since even small mistakes can lead to an incorrect solution. Always double-check your calculations to ensure accuracy. Remember, mastering basic arithmetic lays the foundation for successfully solving more complex equations.