MultiStep Linear Equations Jason Sliwa Most linear equations

Multi-Step Linear Equations Jason Sliwa

Most linear equations require more than one step for their solution. For instance: Solve 7 x + 2 = – 54 I want to get “x” all by itself , first I need to undo the "times seven" and the "plus two". There is no rule about which "undo" I should do first. However, if I first divide through by 7, I'm going to have fractions. Personally, I prefer to avoid fractions if possible, so I almost always do the plus/minus before the times/divide: Then the solution is x = – 8.

Solve 5 x + 7 x = 72 First, I need to combine like terms on the left; then I can solve: Then the solution is x = 6.

Solve 4 x – 6 = 6 x I need to move all the x's over to one side or the other. To avoid negative coefficients on my variables, I usually move the smaller x; in this case, I'll subtract the 4 x over to the other side: Then the solution is x = – 3.

Solve 9 = 3(5 x – 2) First, I have to multiply through the parentheses on the right. Then I can solve: Then the solution is x = 1.

Solve 6 x – (3 x + 8) = 16 Be careful with taking negatives through parentheses. Simplify on the left-hand side first; then solve: Then the solution is x = 8.

Check Your Answers You can always check your work on equation-solving problems. The point of a solution is that it's the x-value that makes the equation true. To check your answer, plug in your solution, and make sure that the equation works. For instance, "x + 6 = – 3", and I got a solution of "x = – 9". Here's the check: x + 6 = – 3 (– 9) + 6 = – 3 So the solution "checks". This ability to check your answers can come in handy on tests. Once you've completed all the questions, go back and plug in your solutions. If the solution "checks", then you know you got that question right. If it doesn't, you have the chance to correct your mistake before you hand in the test!