In Exercises 51–58, solve each compound inequality.

- 11

Question

In Exercises 51–58, solve each compound inequality.

- 11 < 2x - 1 ≤ - 5

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to solve the inequality negative 14 less than three X minus five. Less than or equal to negative three. So in this case we're trying to find the interval for X. So in order to try to break down this two sided inequality I'm going to work with one side at a time. So first I'll work with negative 14 less than three X minus five and then I'll work with the three X minus five less than or equal to negative three. So if I look at that first inequality I have negative 14 Less than three x minus five and I can solve for X by adding five to both sides leaving me with negative nine less than three X. It has become zero. So now I have negative nine less than three X. And I can divide by three. That leaves me with -3 less than X. So that gives me the simplest answer for my left hand side. I'm going to work with the right hand side where I have three acts minus five less than or equal to negative three. And again I'm going to add five to both sides. So I have three X less than or equal to two. And then I can divide by three. That leaves me with X is less than or equal to 2/2/3. So you can see that I have this lower range negative three X. Is greater than that but less than two thirds. So I can write my interval negative three 22 3rd. But in this case notice that there's a difference between their inequalities. In this one we have a less than and in this one we have a less than or equal to. So when you write the notation, it's important to remember that when it has an equal to you have to include the bracket. So this becomes my final interview interval for X. And you can see that this answer aligns with answer choice D. So hopefully this video helped and see you next time.

In Exercises 51–58, solve each compound inequality. - 11 < 2x - 1 ≤ - 5

Key Concepts

Compound Inequalities

Solving Inequalities

Interval Notation

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