What is what does it mean to isolate the variable?

Isolating a variable is a fundamental concept in algebra and other areas of mathematics. It refers to the process of manipulating an equation to get the variable you're solving for by itself on one side of the equation. This allows you to determine the value of that variable.

Here's a breakdown:

• Goal: The primary goal of isolating a variable is to find its value. By having the variable alone on one side, with a numerical value or an expression on the other side, we know what that variable equals.

• Using Inverse Operations: The key to isolating a variable is to use inverse operations. These are operations that "undo" each other. For example:

  • The inverse of addition is subtraction.
  • The inverse of multiplication is division.
  • The inverse of squaring is taking the square%20root.

• Maintaining Balance: Equations must always remain balanced. Any operation performed on one side of the equation must also be performed on the other side. This ensures that the equality remains true.

• Order of Operations (Reverse): When isolating a variable, you generally follow the order of operations in reverse (often remembered by the acronym SADMEP or PEMDAS backwards). This means dealing with addition/subtraction before multiplication/division, and exponents/parentheses last.

• Example:

  Let's say you have the equation: 2x + 3 = 7

  1. Subtract 3 from both sides: 2x + 3 - 3 = 7 - 3 => 2x = 4
  2. Divide both sides by 2: 2x / 2 = 4 / 2 => x = 2

  In this example, we isolated 'x' by first subtracting 3 (the inverse of adding 3) and then dividing by 2 (the inverse of multiplying by 2). The final result is x = 2.

Isolating the variable is a critical skill for solving algebraic%20equations and understanding how variables relate to one another.