Solving Inequalities Using All four Basic Operations

In this video, I want to look at a problem similar to the one we just solved in the last video, but in this problem, we’re going to be dealing with the inequality instead of an equation, and I want to demonstrate how that changes things.

So, let’s take the inequality of 5 – 3x – 3x+2/4 < 12. And so, you remember in an inequality, we have either a less than or a greater than symbol instead of an equal sign.


The following transcript is provided for your convenience.
And so, the rules for solving an inequality are almost exactly the same as those for solving an equation, with one exception. If you multiply or divide by a negative number, you have to flip the inequality sign. So, let’s keep that in mind as we work through this.

So, the first thing we want to do is get x out of this fraction, so we’ll multiply through by 4. 5 times 4 is 20. -3x times 4 is -12x. This, the numerator, stays, because what we’re doing is canceling the denominator, so we have -3x+2, and that’s less than 48.

And so, now, in this one, we have a negative sign outside of our parenthesis, so we need to remember to carry through this negative sign to each term. So, let’s go ahead and rewrite this as 20-12x-3x-2, because you have minus a plus there, so it’s -2, and that’s less than 48.

Okay, now let’s combine our terms, we have -12x-3x, so that’s a -15x, and we have +18, and less than 48.

And so, now, let’s subtract 18 from both sides to get the x term all by itself, and that leaves us with -15x < 30.

Okay, now this is very close to where we were on the last problem, but here, we have a negative on the x side. And so, to get x all by itself, we’re going to have to divide by -15. So, let’s go ahead and divide by -15, that gives us just x on the left side, and it gives us -2 on the right side. But remember that we just divided by a negative number, so that means that our less than sign turns into a greater than sign. So, the solution to this inequality is going to be x > -2.


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