Solving for Variables

What is solving for variables?

Solving for variables involves finding the value of a variable in an equation or inequality. In order to solve for a variable, you will need to isolate the variable on one side of the equation or inequality.

Steps for solving for variables:

Use inverse operations: To isolate the variable, use inverse operations to get rid of any constants or coefficients that are attached to the variable.
Keep equations balanced: Whatever operation you perform on one side of the equation, you must also perform on the other side to keep the equation balanced.
Simplify: Combine like terms and simplify the equation as much as possible.
Check your work: Once you have found the value of the variable, substitute it back into the original equation to ensure that it satisfies the equation.

Examples:

Let's consider an example to illustrate the process of solving for a variable:Example 1: Solve for the variable x in the equation 3x + 5 = 11

Subtract 5 from both sides of the equation:
3x + 5 - 5 = 11 - 5
3x = 6
Divide both sides by 3:
3x ÷ 3 = 6 ÷ 3
x = 2
Check your work:
3(2) + 5 = 11
6 + 5 = 11
11 = 11

In this example, we isolated the variable x by using inverse operations and found that x = 2. When we substituted x = 2 back into the original equation, it satisfied the equation, confirming that our solution is correct.