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Solve Multi-Step Inequalities - Example 3

In mathematics, a linear inequality is an inequality involving a linear function. Linear inequalities are algebraic equations involving the addition, subtraction, multiplication, and division of numbers and variables, and the four basic arithmetic operations (addition, subtraction, multiplication, and division) performed on them. Linear inequalities can be represented graphically using a closed curve (a line segment joining two points) or open curve (a line segment with no end-points).


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so in this example for being asked to salt, given in the quality, and then we'll graph the solution set on the number one. So let's start by solving this inequality. Well, we I see we have lots of sets of parentheses here, so we're gonna use our distributive property a few times. So we're gonna start by bringing down the five. Then we're going to distribute the negative too. Well, negative. Two times eight is negative. 16 and then we have negative two times negative X, which is positive. Two x. There's our plus sign there. All right, then we'll bring down our inequality sign the less son. Next, we're going to distribute the four. Well, four times sex is four X and four times negative. Three is negative. 12. Next, we have another set of parentheses, and in front of it, we just have a negative sign, which remember, means we really have a negative one there. So we need to distribute the negative one. Well, negative. One times two is negative. Two and negative. One times two x is negative. Two x. So now we've removed our parentheses. We'll take a look at the left hand side of your inequality. I see. We have, like, terms there. We have five minus 16, which is negative. 11. So we're gonna be left with negative 11 plus two X is less than. Well, take a look at the right hand side. We have a couple of pairs of, like terms here. First, we have four X minus two X, which is just two X and then we have negative 12 minus two, which is negative. 14. Okay, so the next thing you want to do is collect are variable terms on one side of our inequality. So they do this, I'm going to subtract two acts from both sides of our inequality. Well, two X minus two x zero. So both pairs of these two X's cancel. So if you think back to when you're solving equations, that means we're gonna have some type of special case here. Well, what's left on the left hand side? Well, we have negative 11. We're gonna bring down our inequality sign, Celestine. On the right hand side, we just have negative 14. So let's take a look what we have here. It says that negative 11 is less than negative 14. Well, that's a false statement. Negative 11 is not less than negative. 14 is greater than it. So, just like with solving equations, what this means is that there's going to be no solution. So again there's no value for X that will make our original inequality true.