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

Question

Solve each inequality. Give the solution set using interval notation. See Example 10. -5 < 5 + 2x < 11

Accepted Answer

Welcome back. Everyone in this problem, we want to find a solution set by the inequality negative 39 is less than 24 plus seven X which is less than 94. For our answer choices A is open bracket negative 10, close bracket, B is open bracket, negative nine closed parentheses. 10 union with open parenthesis, 10 infinity, closed parentheses. C is open parenthesis, negative infinity, negative nine closed parentheses. Union with open parenthesis, 10 infinity closed parentheses and D is open parenthesis negative 9, 10 closed parentheses. Now what are we doing here where we're trying to find the solution set for our inequality? I remember that an inequality follows the same logic as solving an equation. The only difference is that we have a solution set instead of just one or two solutions. So if I write my inequality here negative 39 less than 24 plus seven X, less than 94 we can go ahead and solve for X not to get X by itself first, I can subtract 24. But if I subtract 24 from 24 plus seven, X, I'll also have to subtract it from negative 39 and subtract it from 94. No, negative 39 minus 24. That equals negative 63 minus 24. That's zero. So that just leaves us with seven X and 94 minus equals 70. No, I still want X by itself so I can divide through by seven. OK? And no, when I do that negative 63 divided by seven, that's negative 97 X divided by seven is X and 70 divided by seven is 10. Therefore, X is greater than negative nine and less than 10. All we need to do now is to write this in interval notation. So to help us visualize that I'm going to draw our number line and let's put negative nine and 10 on that number line. OK? And no, X is first of all X is greater than negative nine. OK. So X is the least possible value. It could be, it won't be negative nine but it's always greater than negative nine. Likewise X is less than 10. So it, it, it, it's everything below are less than 10. So if I were to represent that here on my diagram would represent our values for X. So X is between our solution set, X is between negative nine and 10. And because it's less than and greater than those would be open and closed parentheses. So our solution is open parenthesis, negative 9 10, closed parentheses which when we look at our answer choices would be answer choice. D thanks a lot for watching everyone. I hope this video helped.

Solve each inequality. Give the solution set using interval notation. See Example 10. -5 < 5 + 2x < 11

Key Concepts

Compound Inequalities

Solving Linear Inequalities

Interval Notation

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