Solve Absolute Value Inequalities - Example 2
Solve Absolute Value Inequalities - Example 3
Solve Absolute Value Inequalities - Example 4
Solve Absolute Value Inequalities - Overview
Solve Compound Inequalities - And Statements - Example 1
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Solve Absolute Value Inequalities - Example 1


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in this example we're being asked to solve the given absolute value inequality. Then we're gonna grab the solution said on a number line. So we're giving the absolute value of X minus five is less than me. Well, just like when solving absolute value equations, the first thing we need to do is isolate our absolute value, which in this case, we have. So what we're gonna do now is set apart to inequalities. So to get the first inequality, we're always going to take what's inside the absolute value, which in this case is X minus five. We're going to keep the same inequality sign less than, and we're gonna keep the stain constant eight. Now, remember, because it's less done sign this is going to be an and statement. So we're going to use the word and in between now, to get our second inequality again, we take the exact expression that's inside the absolute value. So X minus five, we're gonna flip part in the quality sign so the lesson will really become greater. Then we're gonna take the opposite sign of our number eight, which will be negatively. And now we have written our compound inequality. Now we just have to go ahead and solve it. So let's start with X minus five is less than me. Well, to solve for X, we're gonna add five to both sides of our inequality. And a plus five is 13. So what we're left with is X is less than 13. Now, let's solve our second inequality. We have X minus five is greater than negative. So the solve for X, we're gonna add five to both sides of inequality and negative eight plus five is negative three. So we're gonna have X is greater than negative three. So perfect. With solved our inequality. Now we have to graph our solution set on the number line. So we're gonna set up our number line. We're gonna put our two critical values here. We're gonna have negative three and then 13. And for both of them, they're both could be open circles because X has to be less than 13 and bigger than negative three. So we're gonna have open circles at both negative three and 13 and because it's an and statement and we're talking about values that are less than 13 meaning to the left of 13, but greater than negative three to the right than negative three were just shaving in between these two values. So the next thing about absolute value and equalities is you're always for and statements going to shade between the two values that you have. And so now we've graft our number line to represent our solution set.

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