A linear equation of one variable is an expression with terms on both sides of an equal sign (=) and containing only one variable (like x) and no powers or reciprocals of that variable.

Good examples: x = 5 4x - 2 = 8 y + 2 = 94,204,950,029y 100 = z

Bad examples (not linear equations): x2 = 4 2p -3q = 5 47z 2/x = 4

 
So linear equations should be simple to solve in principle, but the details may get you.
THE BASIC STRATEGY: get the variable all by itself on one side of the = and the numbers consolidated on the other side.
THE TACTICS: the Golden Rule of Algebra: You can do anything to one side of an equation, if you do it to the other, too.

For example, you can add the same thing to both sides, or divide both sides by the same thing (except by 0)
REMEMBER that you have to do it to the entire side, not just one term!

Example:

2x + 4 = –x/3 + .5 2x + 4 + x/3 = .5 7x/3 + 4 = .5 7x/3 = .5 – 4 7x/3 = –3.5 7x = –10.5 x = –1.5

This looks strange but it meets our definition. First add x/3 to both sides. –x/3 + x/3 = 0 which can be left out Combine the two terms containing x (add the coefficients) Subtract 4 from both sides Combine the two constants Multiply both sides by 3 Divide both sides by 7. When you have isolated x, what you see is the solution.

This skill in doing these steps is what you have to learn. These are not magical incantations. Each step should suggest itself. See the next page for examples.

examples