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

Question

Solve each inequality. Give the solution set in interval notation. | 5 - 3x | > 7

Accepted Answer

Hello everyone. We're going to solve the inequality. The absolute value of six minus four X. Is greater than 46. Recall that when we have an absolute value, we need to solve two separate inequalities. So first we're going to have 6 -4 x is greater than 46. And we're also going to need to solve 6 -4 X is less than -46. This will give us all of our possibilities for X. That will work within our inequality. So starting off, I subtract six from both sides. So I now have negative four x is greater than 40 after that. I want to get the negative four away from the X. So I'm dividing both sides by negative four. Recall that when you divide both sides by negative you need to flip the inequality so I now have X is less than negative 10 and I'm gonna write what that looks like an interval notation right now, That's like negative infinity to negative 10. So let's see how that works out when we have the other side. So this is half of our solution. We need to find out what the other half is. So for 6 -4 x is less than -46. Again, I'm gonna start out by subtracting six from both sides. This leaves me with -4. X is less than -52. I'm dividing both sides by negative four and again when I divide by a negative I need to flip that inequality so I now have X is greater than and negative 52 divided by negative four is 13. So an interval notation that is saying we have 13 to positive infinity and looking at this to see if there's any sort of overlap. There is not. So we have to take the union of the two and that's answer choice D. So negative infinity to negative 10 Union 13 to positive infinity. Have a nice day.

Solve each inequality. Give the solution set in interval notation. | 5 - 3x | > 7

Key Concepts

Absolute Value Inequalities

Interval Notation

Solving Linear Inequalities

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