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Solving Linear Inequalities - Problem 3

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Solving linear inequalities is very much like solving the linear equations. Try to get x by itself and see what we get as an answer. So for this one is first step we only need to do is distribute. Distribute this 5 through we are left with 5x plus 10, distribute this 4 through, less than 4x minus 4 and this plus x comes down.

Now we combine like terms, nothing we can do on this side let’s combine things over here. 5x plus 10 stays the same this less 10, 5x minus 4. Trying to solve for x we need to subtract 5x from either of the sides. However the times both sides so actually when you subtract it it disappears altogether.

We subtract 5x subtract 5x leaving us with 10 is less than -4. Let’s think about this for a second is 10 actually less than -4? Not really so what’s happening here is we actually have a false statement this isn’t true which means that no value of x will actually work.

Okay I’m going to go back to this statement right here 5x is just a number. Here we have a number plus 10 here we have a number minus 4, there’s no way that when we minus it we are going to get bigger number than we add 10. So what this tells us we work it through and we end up with false statement this tells us this problem has no solution. No values of x will make these true.

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