In Exercises 59–94, solve each absolute value inequality.

|3x + ...

Question

In Exercises 59–94, solve each absolute value inequality.

|3x + 5| < 17

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we need to simplify the inequality five X -10. Less than 20. And we need to express the solution set in interval notation. So in this case we have an absolute value. So an absolute value means that the inner values could be negative or positive. So I'm going to go ahead and sell for both the positive and negative outcomes. So say we have a positive then we have positive five X minus 10. Less than 20. But if we have a negative five X minus 10, less than 20 then I need to divide a negative across inequality. So the inequality switches signs. So from lesson it becomes a greater then and now I have negative 20. So I'm gonna go ahead and solve for both of these inequalities now so adding 10 to both sides, I have five X less than 30 and then X less than six when I divide by the five. So this is one of my first ranges. And if I solve for if the inside was negative I have once again add 10, I have five X greater than negative 10 and then I have X greater than negative two. Once I divide by that five. So now I'm going to draw a number line to sort of visualize these ranges and I'm going to make sure to draw a number line big enough that can capture negative two all the way up to six. So starting negative three negative two negative 1012345, six and seven. So now I can draw In these ranges. So my first one says that X is less than six. So I'm going to go ahead and do a parentheses at six because the X is less than and not less than their eagle too. So I can't do the bracket. And then my second range says X is greater than -2, so I can do another parentheses at -2. And if I connect these two parentheses you can see that that becomes the range for the solution set and I can express that in interval notation It becomes parentheses negative 2 - six parentheses. And that becomes my final answer for the solution set. And you can see that that aligns with answer choice B. So hopefully this video helped and see you next time.

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