2. Solve for   x   and check.

This is a rational equation, and we will run through the steps for solving rational equations. First clear denominators. Multiply both sides by a common denominator. The smallest common denominator is 12. Multiply both sides by 12.

Remove parentheses.

Assemble the surviving factors.

4x - 12 = 3x + 6

Transpose

4x - 3x = 12 + 6

Combine

x = 18

Check

Copy down the original equation

except that wherever you see an   x,   substitute the solution in parentheses.

This simplifies to

or

5 = 10/2

which checks.

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