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Solving Compound Inequalities - Example 3

In mathematics, a compound inequality is a combination of two or more inequalities involving the same variables. The solution of a compound inequality is the set of all values of the variables that satisfy all of the inequalities.

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found inequality for a plus eight is greater than 11. A plus 15 and 13 minus 14 a is less than or equal to 13. Monness three a. So here we have to compound inequalities, so we're gonna work them out to solve each of them individually. So let's start with our first one. So let's get our variable over to the left side. So we're going to subtract 11 a from both sides, so I have negative. 78 plus eight is greater than 15. We're gonna subtract eight on both sides. Negative seven A is greater than seven. The vibe a negative seven means they're sign is gonna flip. So a is less than negative one. Now let's see. Worker Second one again. Let's move our variable over to the left so we're gonna add three A on both sides. So negative 14 plus three a is going to give me negative 11 A is less than or equal to 13. We're going to subtract 13 on both sides, so I have negative. 11. A is less than or equal to zero. We're going to vie by negative 11 and you can have zero. Is your numerator so That's gonna mean our side is gonna flip. A is greater than or equal to zero. Now let's draw out our number one. So we're have zero one to three native, one negative two and negative three. Okay, so let's go ahead and graph. So we have a is less than negative ones. An open circle. It's going to the left and then we have a is greater than or equal to zero and it's going to the right. Well, look at this very carefully. This is an and statement, which means that in a number line, my arrow should be going towards each other. However, my arrows air going in the opposite direction. For this to be an and statement that can't happen, So this is a no solution.

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