What is the order of reverse operations in algebra?

The order of reverse operations in algebra is the reverse of the standard order of operations (PEMDAS/BODMAS). According to the reference material, here's how to reverse operations:

Reversing Algebraic Operations

When solving algebraic equations, we often need to undo operations to isolate the variable. The order in which we reverse these operations is crucial for arriving at the correct solution. Here's the order:

Steps to Reverse Operations:

1. Reverse addition and subtraction (by subtracting and adding) outside parentheses.
2. Reverse multiplication and division (by dividing and multiplying) outside parentheses.

In simpler terms, you undo operations in the opposite order they would be performed according to the order of operations (PEMDAS/BODMAS).

Examples

Let's consider some examples to illustrate this:

Example 1:

Solve for x:

2x + 3 = 7

1. Reverse addition: Subtract 3 from both sides:

   2x + 3 - 3 = 7 - 3

   2x = 4

2. Reverse multiplication: Divide both sides by 2:

   2x / 2 = 4 / 2

   x = 2

Example 2:

Solve for y:

(y - 1) / 4 = 5

1. Reverse division: Multiply both sides by 4:

   (y - 1) / 4 * 4 = 5 * 4

   y - 1 = 20

2. Reverse subtraction: Add 1 to both sides:

   y - 1 + 1 = 20 + 1

   y = 21

Summary

To accurately solve algebraic equations, reversing operations in the correct order is essential. Remember to address addition and subtraction first, followed by multiplication and division.