Variables on Both Sides

When x appears on both sides, move all the x terms to one side and all the numbers to the other.

Which side

Move the smaller x term. Subtracting 2x from 5x leaves a positive coefficient, which is easier to handle.

Whatever you do, do to both

The equation is a balance. Removing 2x from one side without the other breaks it.

Always check

Substitute the answer into the original. Both sides must give the same number.

Gather the variables, then the constants

For 5x + 3 = 2x + 12, subtract 2x to get 3x + 3 = 12, then subtract 3 to get 3x = 9, then divide. A fixed order — variables first, constants second — means you never have to decide what to do next.

Avoiding negative coefficients

Move the smaller variable term, so the one you keep has a positive coefficient. It changes nothing mathematically, but negative coefficients cause errors, and avoiding them costs nothing.

Clear fractions before gathering

Multiply every term on both sides by the least common denominator first. An equation with fractions and variables on both sides has two sources of error at once; clearing one first keeps them from compounding.

Check in both sides separately

Evaluate the left and right sides of the original equation independently with your answer. They must match. Checking one side or a rearranged version misses errors made in the first step.