Solve Multi-Step Inequalities - Example 2
Solve Multi-Step Inequalities - Example 3
Solve Multi-Step Inequalities - Example 4
Solve Multi-Step Inequalities - Overview
Syracuse University
Solve Multi-Step Inequalities - Example 1


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in this example we're being asked to solve to get inequality, and then we'll grab the solution set on the number one. So remember, the first thing we should always do is remove our parentheses by using distributive property. So let's distribute the negative three. Well, negative. Three times two X is negative. Six x and negative. Three times negative. Five is positive 15 now because we're just distributing and we're not multiplying both sides of our inequality by a negative value. We do not flip are inequality sign So it's still going to stay greater than and that will bring down the right hand side four X minus nine minus two x Now, the next thing I'm gonna I see that we have is like terms on the right hand side of our inequality. We have four x minus two x, which is positive two x so I'm gonna bring down the negative six x plus 15 and it's greater than two X minus nine. Okay, so the next step we need to do is gather are variable terms on one side of the inequality. So to do this, I'm going to subtract two x from both sides of our inequality. And again you could be removed the negative six x to the right hand side. Or as I'm doing, I'm moving the two x to the left hand side. Well, negative six x minus two X is negative, Adx. So we're left with negative adX plus 15 is greater than negative night. And as you can see, we now have a two step. So I'm going to start by subtracting 15 from both sides of our inequality. So we have negative nine minus 15, which is negative. 24. So we're left with negative. Adex is greater than negative 24. So now, to get X by itself, we're going to divide both sides of our inequality by negativity. Now, no, this We're dividing both sides of our inequality by a negative value. I apologize. Of course you got away from me there. So because we're dividing both sides of our inequality by a negative value, we need to flip our inequality sign. So we're not gonna have a greater than sign anymore. We're gonna have a lesson sign. So we're gonna be left with X is less than well, negative 24 divided by negative eight is positive three. So now we've solved their inequality. Our solution is that X is less than three. So now what we want to do is graph our solution on a number line. So let's go ahead and set up our number line here. We're gonna put our key number three here in the middle now, because three is not a solution, there's going to be an open circle. And we want all the values of X that are less than three, which would be to the left on the number line. So we're going to shade the left hand side of our number line. So now we have solved and graph our original inequality.