Solve each inequality. Give the solution set using interval no...

Question

Solve each inequality. Give the solution set using interval notation. See Example 10. 10 ≤ 2x + 4 ≤ 16

Accepted Answer

Welcome back. Everyone in this problem, we want to find a solution set for the inequality 41 is less than our equal to eight X plus 17, which is less than our equal to 73. And we want to express our answer in interval notation for our answer choices A is open parenthesis seven infinity, close parenthesis, B is open parenthesis, negative infinity. Three closed parentheses, C is open bracket, 37, close bracket and D is open parenthesis 37 closed parentheses. Now we want to find the solution set to our inequality. And remember that to solve inequalities, we use the same logic as solving equations. The only difference is that we have a solution set, not just one single solution. So let's see if we can figure out that set. And then let's see if we can write it in interval notation. So I'm going to rewrite my inequality here. And let's see if we can solve for X. Now, if I want to get X by itself, I can divide, I can subtract 17. But if I subtract 17 from inside the boundary for any equality, I'll have to subtract it on the left side of the boundary. And on the right side of the boundary, no 41 minus 17 equals 24 17 minus equals zero. So I'm just going to be left with eight X and 73 minus 17 equals 56. I still don't have X by itself, but I can divide through the entire inequality by eight because eight X divided by eight leaves us with X and 24 divided by eight equals 3 56 divided by eight is seven. Therefore, X or rather three is less than our equal to X, which is less than our equal to seven. In other words, X is between three and seven. So how can we represent this in interval notation? Well, let's visualize what's happening here. So let's draw our number line and on our number line, we'll have three up to seven. And what we're saying is that X is between three and seven, X is greater than, or equal to three. So that means it could be three and it's less than, or equal to seven. So that means it could be seven or less. That means our interval would be open bracket, three and seven, close bracket, which if we look at our answer choices, that would be answer choice. C thanks a lot for watching everyone. I hope this video helped.

Solve each inequality. Give the solution set using interval notation. See Example 10. 10 ≤ 2x + 4 ≤ 16

Key Concepts

Compound Inequalities

Solving Linear Inequalities

Interval Notation

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