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Solve Inequalities Using Multiplication and Division - Example 3

In mathematics, an inequality is a conditional statement that is either true or false, depending on the value of the variable.

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So in this example, we're being asked to solve the given inequality. And then we're gonna graft a solution, said on a number line. So our inequality says negative two is less than or equal to X, divided by negative three. So remember, we solve inequalities just like we would equations. So because X is getting divided by negative three, we need to multiply both sides of our inequality by negative three, because then the negative threes will cancel out. Now, don't forget, because we're multiplying both sides of our inequality by a negative value, we're going to need to flip our inequality sign around. Therefore, the less than or equal to sign is going to become greater than or equal to. Now, on the left hand side of the inequality, we have negative three times negative two, which is positive. Six and on the right hand side of the inequality are negative. Threes canceled out. So we're just left with ax so perfect, we've now solved our inequality. Let's make that X a little better. There we go. All right, Now that we're salt, we want to graph the solution set on a number line. So we'll set up our number line are critical. Number of positive six will go in the middle. Yeah. Then we'll determine. Should we have open or close circle? Well, because six is greater than or equal to six, it is part of our solution set. So we're gonna have a close circle here in six. Now, the last thing we need to do is figure out should be shade to the left or to the right. Remember, with inequalities we wanna have are variable go first. So if we were the flip this around and have XP first in 60 seconds, notice how the arrows pointing to the X so we would have to flip it around. So we really have X is less than or equal to six. So where the values of X that are less than or equal to six. That would be to the left on our number line. So we're going to shade to the left hand side of our number line. So now we have solved and graft the solution set to our original inequality