# How to Use Equations

Equations are a fairly easy bit of math that can be used for a great number of things. While studying algebra, we disliked learning and then memorizing equations. We always felt we would never need it, once we graduated. We were wrong, because we use equations many times during our lifetime.

## Steps

- 1
**Find something you can use an equation to solve.**This will determine the meaning of your equation. Unless you're dealing with algebra by itself, your equation will be useless if you don't know what it means. An example of a useful equation is**.15p = t**, which will determine how much tip(t) you should give for a meal that costs p. - 2
**Define your variables.**In the example above, p is the price of the meal, and t is the tip given. - 3
**Figure out which variable is independent and which one is dependent.**- The independent variable will be the "input" of the equation; basically, it will determine the dependent variable. In the example, this would be the price of the meal, because it is what determines how much tip you should give.
- The dependent variable will be the "output" of the equation; basically, it depends on the independent variable. In the example, this would be the tip you should give, because it is determined by how much the meal costs.

- 4
**Set the domain of the equation.**Variables can be*anything*, but in most cases not every value of a variable would make sense for the situation described by the equation. In the example, you can exclude any negative values and zero, because you'll never have to pay a negative amount for a meal, and if it's free, you don't have to pay a tip. - 5
**Know what you're solving for and know what you're given.**Usually you'll be trying to solve for the dependent variable when you're given the independent variable, but sometimes you'll need to solve for the independent variable when you're given the dependent variable. In the example, you could either be trying to figure out how much you'll have to tip for a meal that costs something like $10.00, or you could be trying to figure out how much a meal would cost if you had to tip $5.00. - 6
**Write the equation, if you haven't already.**This will help organize your thoughts. - 7
**"Plug in" your known integers every time they appear in the equation.**This means that if you know the cost of the meal, put that everywhere you see a p in the equation.**.15p = t**would become**.15(10.00) = t**if the price of the meal is $10.00. - 8
**Algebraically solve for the unknown.** - 9
**Check your answer.**Ask yourself if your answer makes sense. Does paying a negative tip make sense? Does paying a $50.00 tip for a salad that cost $2.00 seem reasonable? If it doesn't, you need to review your work, and see if you made any errors. Check your calculator's memory if it seems like you didn't make any errors on paper. - 10
**State the answer.**Once you're reasonably sure about your answer, go ahead and use it for whatever you need it for.

## Tips

- Always remember to follow the order of operations.
- If you have a hard time doing this, talk to a teacher or tutor.
- Practice! This won't happen overnight. Keep practicing it until it becomes second nature.
- Show your work. If you made a mistake, it's easier to go back and find out where in the process you made one instead of doing the whole process over again. If you're in a classroom setting, usually your teacher will at least give you partial credit if you get it wrong while still doing the process correctly.

## Warnings

- Don't rush through things. You'll probably make mistakes when you do.

## Sources and Citations

- Purple Math
- Definition of an equation
- Cheat sheets with common equations

## Article Info

Categories: Algebra