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

Question

Solve each inequality. Give the solution set in interval notation. . | 3x - 4 | ≥ 2

Accepted Answer

Hello everyone. We're going to solve the inequality. The absolute value of seven X -2 is greater than or equal to 12. Recall that when we're doing absolute values we need to solve two different inequality expressions. This means we have both seven X -2 is greater than or equal to 12. But we also need to solve seven X - Is less than or equal to -12. This will give us all the possibilities for our X value. So starting with seven X -2 is greater than or equal to 12. I'm gonna add two to both sides. So seven x is greater than or equal to 14, Dividing both sides by seven. I get the X. Is greater than or equal to two. So this is an important part of our solution. Our answer is going to need to be an interval notation so it's not gonna look exactly like that but it will help us find our answer Next for seven X -2 is less than or equal to 12 or sorry, less than or equal to negative 12. We're gonna add 2 to both sides. So we get seven X is less than or equal to negative 10, Dividing both sides by seven. I get that X is less than or equal to -10/7. So this is the other part of our solution but now we need to put this in interval notation. So looking at it We know that our values have to be less than or equal to negative 10/7 so that would be negative infinity to negative 10/ and we know that it has to be greater than or equal. I apologize. I put the wrong bracket there. We also know what needs to be greater than or equal to two, so that means it includes two and continues to positive infinity. So the answer choice that combines the two things we have there is answer choice B negative infinity to negative 17th. Union with two to positive infinity. Have a nice day.

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Solve each inequality. Give the solution set in interval notation. . | 3x - 4 | ≥ 2

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