Solve each inequality. Give the solution set in interval notation...

Question

Solve each inequality. Give the solution set in interval notation. | 0.01x + 1 | < 0.01

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to try to find the solution set for the absolute value inequality, absolute value of 0.9 X. Plus 0.9 less than 0.72. So in this case we're working with an inequality that has an absolute value. So we want to think about what the absolute value does to the components inside. So the absolute value means that we could either have a positive number inside. So we could have positive 0.09 x plus 0.9 less than 0.72. But we could also have negative 0.9 X plus zero point nine Less than 0.72. So in order to find the solution set we need to solve for both of these scenarios. So if I look at the positive side first I'll start by subtracting 0.9 from both sides. Because recall that for the solution set, I'm trying to find the values of X. That make this inequality true. So I'm going to be solving for X. So when I subtract 0.9 I left with 0.9 X. On the left hand side and the right hand side is now negative 0.18 and then I'll divide by 0.09. That leaves me with X is less than negative two. So now I've simplified the inequality. If the values inside the absolute values are positive. Now I want to look at if they were negative and the first thing I'm gonna do because there's this negative on the outside, I'm going to divide Everything by - and notice how I'm dividing by a negative across the inequality so it changes sign or direction. So instead of being less than it's now going to be greater than and this negative cancels out. So I'm left with 0.9 X plus 0.9 is greater than negative 0.72. And again I'm gonna want to isolate X. So I'll subtract 0.9 From both sides. So when I subtract I have 0.09 X on the left greater than negative 1.62 and two finally isolate X all divided by 0.09. So that means that X is greater than negative 18. So now I have two inequalities for X. X has to be less than negative two and X has to be greater than negative 18. So I'll start with the negative two. So because X is less than negative two, negative two is a maximum. So I'll write it on the right side of my interval with a parentheses and not a bracket because there is no equal to. And my second inequality is telling me that X has to be greater than -18, which means that -18 is a lower boundary. So I can write it on the left hand side of my interval and again a parentheses because there is no equal to. So the solution set for this absolute value inequality is negative 18 to negative two, and you can see that answered choice A also has that same interval, so hopefully this video helped and see you next time.

Solve each inequality. Give the solution set in interval notation. | 0.01x + 1 | < 0.01

Key Concepts

Absolute Value Inequalities

Interval Notation

Solving Linear Inequalities

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