Strategies to solve simple math equations

What are the strategies for solving simple equations?

I got this question in the mail just today.

I assume the person means LINEAR equations - those where you only have one variable (usually x), and that x is not raised to second or third or any other power, nor is it in the denominator or under square root sign or anything. Just x's multiplied by numbers and numbers by themselves, such as:

2x - 14 = 9x + 5

OR

1/3x - 3 = 2 - 1/2x

OR

2(5x - 4) = 3 + 5(-x + 1)

Here are the strategies for solving these:
* You get rid of paretheses using distributive property
* You may multiply both sides of the equation by the same number
* You may divide both sides of the equation by the same number
* You may add the same number to both sides of the equation
* You may subtract the same number from both sides of the equation

You might think, "Which one of those will I use, and in which order?"

That depends. There is no clear cut-n-dried answer.

Whatever you do, you try to transform your equation towards the ultimate goal: where you have x on one side alone. Also whatever you do, your goal is to transform the equation to one that you already know how to solve. It might take several steps.

For example, your first step with these equations, could be to...
1/3x - 3 = 2 - 1/2x... multiply both sides by 6 to get rid of the fractions
2(5x - 4) = 3 + 5(-x + 1)...multiply out the parentheses
2x - 14 = 9x + 5...add 14 to both sides (or subtract 9x)
1/4(2x - 27 + 0.5x) = 2/5(8x + 3)...multiply by 20 to get rid of the fractions

As with most things, practice makes perfect. Check also the websites below:

Tutorial on linear equations has a 4-step strategy for solving linear equations which summarizes it real well.

Algebra 1 Review - Solving Simple Equations - a step-by-step slideshow.

Ask Dr. Math ® - Solving simple linear equations - lots of examples to read here.


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