Solving Linear Equations
From when you very first learned how to add and subtract, you have been solving equations. The difference in Algebra 1 is that when we solve an equation, we place a variable in for the number that we do not know. For example, if a first grader needs to figure out what 4 + 9 is, then the Algebra 1 equivalent problem could be something like 4 + 9 = x, and we need to solve for x. When we’re given an equation that has a variable in it, and we are asked to solve the equation, we are really just figuring out which values for the variable will make the equation true. For example, in our 4 + 9 = x case above, x = 13 makes the equation true because if we put 13 in place of x and simplify everything, then we end up with a true statement of 13 = 13.
All of Algebra 1 is based on the ability to solve these basic equations. Later on when you’re solving more difficult equations that are fairly complex in nature, the basics of solving simple equations will guide you to the correct answer quickly. If you don’t learn these basics well, then later on you will be very confused and find it difficult to catch up. Learning to solve equations is much like constructing a building in that you have to start with a strong foundation. It doesn’t matter what you build on top of your foundation since if the foundation falls then the rest of the building falls as well.
When learning to solve these equations, you’re going to be looking at mathematics in a way that you’ve never had to before. Instead of having a straight-forward path to solving a problem that is mechanical in nature, you’ll actually start to have to think about general strategy. If you know in general what you are trying to do with an equation to be able to solve it, then your confidence will be boosted and you will find it much easier to solve the equations in question.
The Nature of Equations – If you understand what equations are and how they work, solving equations is much easier.
The Nature of Equations (Video) – A short video presentation explaining this critical concept.
One Step Equations – The most basic equations only require one step to be able to solve.
Two Step Equations – More complicated equations can take two or more steps to solve.
Variables on Both Sides – Here we look at how to handle situations where there are variables on both sides of an equation.
Solving Inequalities – There are some small, but important, differences between solving equations and solving inequalities.