Strategy for Solving a Linear Equation with One Variable
Strategy:
1. Clear fractions by multiplying both sides of the equation by the LCD 2. Simplify each side of the equation by removing the brackets 3. Combine the like terms on each side 4. Isolate the variable you are solving for (e.g. x) by performing the same operation on both sides of the equation 5. Get a numerical coefficient of 1 for the unknown variable by multiplying/dividing 6. Check the solution using the original equation and the root
Golden Rule: Whatever you do to one side of an equation, you must do the exact same thing to the other side.
Example
(x  8) / 5 + 8 / 5 = x / 3
15[(x  8) / 5 + 8 / 5] = 15[x /3]
15 (x  8) / 5 + 15 (8 / 5) = 15 (x / 3)
3(x  8) + 3 (8) = 5x
3x  24 + 24 = 5x
3x = 5x
3x  3x = 5x  3x
0 = 2x
0 / 2 = 2x / 2
0 = x
Check:
(0  8) / 5 + 8/5 = 0 /3
8/5 + 8/5 = 0 / 3
0 = 0
Therefore the solution that was found is correct because both sides of the equation are equal upon substitution
