Solving for the Same Variable on Both Sides of the Equal Sign
When you have x (or any variable) on both sides of the equal sign, you need to get the variable alone on one side and all the numbers on the other. This is called "isolating the variable." If you can solve for a variable on one side of the equation, you can solve for the same variable on both sides. Remember to use inverse operations to "move" terms or numbers from one side of the equal sign to the other. You must also remember that whatever you do on one side of the equal sign must also be done to the other side to keep the balance.
6x + 3 = 8x - 21
subtraction -3 -3
6x = 8x - 24
subtraction - 8x - 8x
- 2x = - 24
division -2 -2
x = 12
This tutorial starts by reviewing solving for a variable on one side, then moves on to a variable on both sides of the equation. http://cnx.org/content/m18033/latest/
And this tutorial jumps right into it: http://cstl.syr.edu/fipse/algebra/unit3/combine.htm
Sometimes you will get a weird answer. If you get something that is true, such as 2 = 2, that means that there is an infinite number of answers; any number you pick will work when you substitute it into that equation. If you get something that isn't true, such as 0 = 3, that means there is no solution; no number you substitute in for your variable will work. http://www.jamesbrennan.org/algebra/intro%20to%20algebra/solutions_of_algebraic_equations.htm
PRACTICE
Now try some exercises. http://www.onemathematicalcat.org/algebra_book/online_problems/solve_lin_int.htm#exercises
ASSESS
Test yourself: http://teachers.henrico.k12.va.us/math/hcpsalgebra1/Documents/3-4/solvequvarbothsides.htm
And now try to win $1,000,000! http://www.quia.com/rr/42586.html Don't forget to post how you did in the gaming forum below.
You are ready to move on to Solving for Several of the Same Variable.
6x + 3 = 8x - 21
subtraction -3 -3
6x = 8x - 24
subtraction - 8x - 8x
- 2x = - 24
division -2 -2
x = 12
This tutorial starts by reviewing solving for a variable on one side, then moves on to a variable on both sides of the equation. http://cnx.org/content/m18033/latest/
And this tutorial jumps right into it: http://cstl.syr.edu/fipse/algebra/unit3/combine.htm
Sometimes you will get a weird answer. If you get something that is true, such as 2 = 2, that means that there is an infinite number of answers; any number you pick will work when you substitute it into that equation. If you get something that isn't true, such as 0 = 3, that means there is no solution; no number you substitute in for your variable will work. http://www.jamesbrennan.org/algebra/intro%20to%20algebra/solutions_of_algebraic_equations.htm
PRACTICE
Now try some exercises. http://www.onemathematicalcat.org/algebra_book/online_problems/solve_lin_int.htm#exercises
ASSESS
Test yourself: http://teachers.henrico.k12.va.us/math/hcpsalgebra1/Documents/3-4/solvequvarbothsides.htm
And now try to win $1,000,000! http://www.quia.com/rr/42586.html Don't forget to post how you did in the gaming forum below.
You are ready to move on to Solving for Several of the Same Variable.