In Exercises 103–104, use the graph of y = |4 - x| to solve each ...

Question

In Exercises 103–104, use the graph of y = |4 - x| to solve each inequality.

|4 - x| ≥ 5

Accepted Answer

Hey everyone in this problem we are asked to solve the given inequality. Using the graph shown the inequality we're given is the absolute value of X plus two is greater than or equal to one. Alright if we look at this graph in green we see that this is the graph Of the absolute value of X-plus two. Now our inequality we want them to be greater than or equal to one. Ok. So when we're looking at inequalities on a graph, okay, We have X plus to the absolute value drawing green and we want to draw the line. Why equals one? Okay. And the line y equals one. Gonna be the horizontal line. Them drawing in black here. Why equals one? No, we're looking at the solution. Okay. We want the absolute value of X plus two to be greater than or equal to one. So if we want it to be greater than or equal to one we want this portion of the function. Okay, we're the absolute value of X-plus two is above the line. Like was one that we drew. And if we look at the corresponding X values it's gonna be the X values at negative three K. Including negative three into the left And then including negative one into the right. Okay. That's where we have X values that allow this function and the absolute value of exports to to be greater than one. So if we were to write this out in interval notation. Okay we have all of the X values less than or equal to negative three. Well that's gonna be negative infinity. Up to negative three. Can we use a square bracket on negative three to show that it's included. Okay. And it's included because we have greater than or equal to one. Ok. At one we have an X. Value is negative three. So we can include that value. And then we also have the interval starting at negative one. And including negative one. Again square bracket because we're including that value because we can be at one. Okay. All the way up to positive infinity. Alright. So if you look at our answer choices, we see that we're gonna have answer choice. See here we have the interval from negative infinity up to including negative three. Okay. And the union with the interval from negative one. Including negative one. All the way up to positive infinity. Okay. That's where that function. The absolute value of X plus two is above that line. Like was one that we drew. That's it for this one. Thanks everyone for watching. See you in the next video

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In Exercises 103–104, use the graph of y = |4 - x| to solve each inequality.
|4 - x| ≥ 5

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