Solving algebraic equations boils down to one simple concept: solving for the unknown. The basic idea behind how to do this is simple: what you do to one side of an equation, you must do to the other. As long as you perform the same operation on both sides of the equation, the equation remains balanced. The rest is simply performing a series of arithmetic functions to break apart the complex equation in an effort to get the variable x by itself.
Write down the equation in its simplest terms. This concept may sound daunting, but by taking away complex functions like square roots and exponents, you drastically reduce the complexity of the problem. For example: 2t - 29 = 7. This equation is already expressed in its simplest terms and is ready to be taken apart and solved.
Begin solving for x. The basic principle behind algebra is to get the variable (x) on one side by itself and a number on the other side of the equals sign. The solution to any algebra problem should ultimately look like this: x=(any number), where x is the unknown variable and (any number) is what is left over after a series of mathematical functions. In order to accomplish this, you must perform a series of calculations on both sides of the equal sign. The only rule here is to make sure that what you do to one side, you do to the other. This keeps the algebraic sentence true. For example, if you add 29 to the left side in order to isolate t, you must also add 29 to the right side to balance the equation.
2t-29=7 2t-29+29=7+29 2t=36
Continue to isolate t by removing calculations, one by one. The next step in this example would be to divide both sides by two.
t=18 Now you have solved the equation.
Check your answer. In order to make sure that you have solved the problem correctly, plug your answer back into the original problem. After performing the calculations required to solve for t, calculate the original problem by substituting t with your answer. For example:
The answer balances. This equation is solved.
The only mistake you can make in solving algebra equations is to unbalance the equation. As long as you are performing the functions to both sides, the process will be correct, though it may take you more steps to solve for the unknown.