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Basic Algebra

Basic Algebra

At a Glance - Solving Two-Step Equations

Solving two-step equations is not much more complicated than solving one-step equations; it just involves an extra step.

Usually there is more than one way to solve these. It's ok to use whatever method makes most sense to you. The general rule of thumb when isolating the variable is to undo the order of operations, PEMDAS. Start with addition and subtraction, then multiplication and division, then exponents, and finally parentheses.

Let's look at an example: 2x - 6 = 12

Method 1

2x-6=12
2x -6 +6 = 12 + 6add 6 to each side
2x = 18
2x/2=18/2divide each side by 2
x=9

Method 2

2x -6 = 12
(2x-6)/2= 12/2divide each side by 2
2x/2 - 6/2 =12/2separate the fractions
x - 3 = 6simplify
x - 3 + 3 = 6 + 3add 3 to each side
x=9

Check the answer:

2(9) - 6 = 12

18 - 6 = 12

12 = 12

w00t!

Personally, we think that the first method is easier, since we don't have to worry about separating the fractions. It is also the method that follows the rule the best, and first gets rid of the least connected number (the 6).

Example 1

Solve for x:

-3x - 7 = -12


Example 2

Solve for y:

1 -3y = -14


Example 3

Solve for x:

(x+5)/2 = 10


Exercise 1

Solve for z: -12x + 18 = -18


Exercise 2

Solve for c: (c-7)/4 = -1


Exercise 3

Solve for g: 10 - 2g = 0


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