Solving single variable problems (basic algebra)
A single variable equation looks something like this: 3 x + 4 = 2x + 12 or this: x^2 = 144
Here are some foundations you need: 1. know orders of operations (GEMS or PEMDAS). That means, you need to know what to do first. (GEMS is Grouping, Exponent, Multiplication/division and Subtracting/adding. PEMDAS is Parenthesis, Exponents, Multiplication, Division, Addition and Subtraction).
2. Know your goal is always to "isolate" the variable, get it alone on one side of the equation.
3. Combine like terms early in the solving process.
4. Remember the rule: "you must always keep the equation balanced, by doing the same operation on both sides."
5. Use shortcuts! There will be plenty of opportunities for that!
6. Know when to use your calculator and when math facts serve you better.
OKAY! Let's solve 3 x + 4 = 2x + 12. Note, there are no parenthesis and no exponents. So, first combine like terms: 3x and 2x (multiples of the same variable) and 4 and 12 (numbers!)
"move" 2x to the right side by subtracting it from both sides (rule 4 above). Our new equation:
3 x - 2 x + 4 = 2 x - 2 x + 12. simplifies to x + 4 = 12. (wow! That's a lot closer to solution.)
Now I can follow rule 2, 3 and 4 all at once by subtracting 4 from both sides: x + 4 - 4 = 12 - 4.
Our solution is x = 8!