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.