Solving Linear Equations w/ Parentheses

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Once you've learned the basics of solving linear equations, your textbook and instructor will start throwing exercises at you that involve parentheticals which usually need first to be simplified (or "expanded", which means that you've multiplied through and then simplified the result).

• Solve 9 = 3(5x − 2)

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• Solve 6x − (3x + 8) = 16

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• Solve 7(5x − 2) = 6(6x − 1)

For equations with parentheticals, take your time and write out all of your steps, like I did above. Don't try to do everything in your head.

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• Solve 3(x − 2) = 6

If I hadn't noticed that I could start by dividing through, I still would have gotten the right answer, eventually. But if it's possible to divide through, giving myself smaller numbers to work with, I do like to take advantage of that. This simplification doesn't occur often, but try not to be blind to it, the few times that it does pop up.

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• Solve 13 − (2x + 2) = 2(x + 2) + 3x

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Don't forget: There is never any reason to be unsure of your solution to a linear equation, because you can always check your answer. The meaning of the solution value is that it is the x-value that makes the equation true. So, to check your answer, you plug your solution value back into the original equation, and you make sure that the equation "works" with that value. For instance, in the last exercise above, my solution was x = 1. To check my solution, I'll plug my value into the left-hand side (LHS) and right-hand side (RHS) of the original equation, and make sure that both sides evaluate to the same number.

The two sides of the equation evaluate to the same value, so the solution "checks", and I now know that my answer is correct

By the way, if possible, you should try to check your answers when you take tests. Once you've completed all the questions (assuming you've got some time left over), go back and plug your solutions back into the original question. If your solution to a given question "checks", then you know you got that question right. If it doesn't check, then you have the chance to correct your mistake before you hand in your test.

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You may need to solve linear equations with nested parentheses, too.

• Solve 2[3x + 4(3 − x)] = 3(5 − 4x) − 11

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• Solve 3[x − 2(3x − 4)] + 15 = 5 − [2x − (3 + x)] − 11