In all exercises, other than exercises with no solution, use i...

Question

In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 4(3x - 2) - 3x < 3(1 + 3x) - 7

Accepted Answer

Hello everyone in this video. We're going to be looking at this practice problem where we want to solve the linear inequality six times two X minus four minus two X. Less than five times one plus two X minus 10. And we want to express the solution set in interval notation and then graph it on a number line. So in order to find the solution set, we want to try and isolate X. Which means we basically want to solve for X. But with the inequality. So if I write our inequality to the right here, you can see that I have some parentheses. So I'm going to go ahead and follow pen does and deal with the parentheses first, which means I want to distribute this six and this five to the parentheses. So I'll have six times two. X is 12 X. Six times negative four is negative 24 minus two X. Less than five times 1. Which is five Plus five times x. is 10 x and minus 10. So if I combine like terms on each side, I have 12 X minus two X. So this becomes 10 x minus 24 less than 10 X. And I can combine the five and the negative 10 leaving me with negative five. So now I can move terms like terms to each side will do plus minus 10 X. Well it seems like positive 10 x minus 10 X. Leaves zero X less than negative five plus 24 is 19. So this becomes. zero is less than 19. And you can see that there's no X variable left in my expression. But because zero less than 19 is a true statement, I can say that this inequality is true for all real numbers, which means that if I expressed that solution set in interval notation, I can go from negative infinity to positive infinity. And if I were to transfer that to a number line, it would look So you draw a number line here say this is zero, I'll say this left tick is negative 10 and this right tick is positive 10. Well, my my interval would look like a line that extends through all of that with an arrow because it can go to negative infinity and positive infinity. So if we look at the answer choices, you can see that answer choice B two notes what I just described. So that becomes our final answer. So hopefully this video helped and see you next time.

In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 4(3x - 2) - 3x < 3(1 + 3x) - 7

Key Concepts

Solving Linear Inequalities

Properties of Inequalities

Interval Notation and Graphing Solutions

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