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Solve Inequalities Using Multiplication and Division - Example 2

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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Video Transcript

So in this problem, we're being asked to solve the giving them the quality. And then we're going to graft the solution set on a number line. Well, our inequality says X is getting divided by eight. And it is greater than negative, too. So again, we're going to solve, just like we within equation. So how do we undo dividing by eight? Well, that would be to multiply by eight. So we're gonna multiply both sides of our inequality by positive, because the eights on the left hand side will cancel out. So we're left with exes. Well, now we're multiplying both sides of our inequality, but because we're multiplying both sides by a positive eight are inequality sign will not change. So it's still going to stay greater than now. We just multiply like normal. Negative. Two times eight is negative. 16. So remember on Lee, if you multiply both sides by a negative value, would you switch it? Okay. Perfect. Now we've solved our inequality. Now, the next thing the directions ask us to do is graft the solution set on a number line. So we'll set up our number line are critical number negative 16 will go in the middle, then we'll determine if we need to open a coast circle. Well, because negative 16 is not a solution. We're gonna have an open circle. Then we'll determine if we shade to the left or to the right. Well, because X has to be greater than negative 16, the values of X will be to the right of negative 16 on the number line. So we're just going to shade in the right hand side of our number line. So now we have solved and graft the solution set to our original inequality.