Solving equations with one or more variables is a crucial skill in math and science. The concept of solving equations can be applied to many real-world situations, such as calculating the amount of time it will take to travel
An equation is simply a mathematical representation for two things that are equal. This equality allows us to solve for unknown pieces of the equation. These unknown values are called variables. There are three steps required to solve most equations:
These are the general steps for solving an equation with variables:
Step 2: Move all of the parts containing the variable you are solving for to the same side of the equation.
Step 3: Isolate the variable using inverse operations.
The main objective when solving an equation is to isolate the variable. When the variable is on its own, it reveals the solution. The solution of an equation is a value that makes the equation balanced. For example, in the equation
Many equations will have only one variable, as in the previous example. However, some equations will have more than one variable.
Example 1
Let’s look at a few examples of equations with more than one variable.
The equation
Now the goal is to isolate the variable
Now we are only one step away from knowing the value of
“Undoing” operations is referred to as inverse operations. Inverse operations are like opposite operations. The inverse of adding
Example 2
Let’s look at another example of an equation with multiple variables. This equation is often seen in the world of geometry. The equation is used to find the area of a circle, and it states that
When the values are plugged into the equation,
Formulas involving speed, area, or radius are only a few examples of the value of solving for variables. This skill is widely used in the world of math and science, so it is important to become familiar with the process. Remember, the main objective is to isolate the variable, which usually involves using inverse operations.
Solving for Variables Sample Questions
Here are a few sample questions going over solving for variables.
Solve the equation for
Solve for the variable
A phone company charges new customers a one-time installation fee of
Dan wants to build a small wooden box that has a volume of
Volume Formula for rectangular prisms:
The rate formula is