Variable
posted by seth .
SOLVING EQUATIONS WITH THE VARIABLE ON BOTH SIDES
Solve the equation. Then check your solution.
4x9 = 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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