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April 27, 2015

Homework Help: Variable

Posted by seth on Saturday, August 5, 2006 at 11:22am.

SOLVING EQUATIONS WITH THE VARIABLE ON BOTH SIDES

Solve the equation. Then check your solution.

4x-9 = 7x+12


Just remember that one can add, subtract, multiply, divide, etc but whatever is done to one side must be done to the other side of an equation.
4x - 9 = 7x + 12.
Add 9 to both sides.
4x - 9 + 9 = 7x + 12 + 9.
Combine terms.
4x = 7x + 21.
Now subtract 7x from both sides.
4x - 7x = 7x -7x + 21.
Combine terms.
-3x = 21.
multiply both sides by -1.
-1(-3x) = -1(21).
Perform the operation.
3x = -21.
Divide both sides by 3.
3x/3 = -21/3.
Perform the operation.
x = -7.
To check, substitute -7 for x in the original equation and see if that satisfies th equality.
4x - 9 = 7x + 12.
4(-7) - 9 = 7(-7) + 12.
-28 - 9 = -49 + 12.
-37 = -37.
I hope this helps. If you don't understand anything about the solution, please repost but tell us exactly what you don't understand.


Thank you!!


After you see how this is done, a shortcut may be taken as follows:
To move any term from one side to the other, simply change the sign. That is, 4x - 9 = 7x + 12.
Just move the 9 to the right side but change to +9. Move the 7x to the left side by making it -7. Then combine terms and solve for x.
4x - 7x = 12 + 9
-3x = 21.
Now change the sign on both sides.
3x = -21.
x = -21/3 = -7.
This procedure usually is much quicker than the first one but the first one shows you how it all works.

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