In Exercises 105–106, use the table to solve each inequality.

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Question

In Exercises 105–106, use the table to solve each inequality. - 3 < 2x - 5 ≤ 3

Table showing values for x and y=2x-13 for solving linear inequalities.

Accepted Answer

Hello, everyone. In this video, we're going to be looking at this practice problem which states solve the given inequality using the table below. And the inequality is two less than or equal to two X -13, less than 10. And in the table below, we have a row for X values and a row for Y values and zero for X values includes 7 halves, 8, 17, halves, 9, 19 halves, 10, 21 House, 1123 House and 12. And those correspond to the numbers one through 11 on the wire. Oh So for the inequality, we want the values of why to fall between two and 10. And I say the values of why? Because if you look at the notation for Y Y is equal to two X minus 13. Well, our inequality is two less than, or equal to two X minus 13, less than 10 Where we can replace the two X -13 with Y. So in reality, we're looking for two less than or equal to Y, which is less than 10. So that means I want to find the values where Y falls between two and 10. So if we go to this table, Well, why is equal to two here? And why is equal to 10 in this second to last column? So I can draw a line that sort of spans through that region. And I need to figure out if I should include the endpoints. So the first inequality is to less than or equal to why? Which means I can include that too. And the second one is just less than 10. So if I were to draw Number line, it would be an open circle or I don't include 10. So the regions where Y falls between two and 10, X is equal to 15/2 and 23/2. So those also represent the solutions for the inequality. And recall that I said the lower boundary that too would have to be equal to. So I can draw a bracket. So I'd have bracket 15/2 all the way up to 23/2, but with a parentheses. So this becomes my final answer for this practice problem in this range of X values Y or two X minus falls between two and 10. And if we look at the answer choices, you can see that answer choice. A also has the same notation with bracket halves, 2/23/2, parentheses. So hopefully this video helped and see you next time.

In Exercises 105–106, use the table to solve each inequality. - 3 < 2x - 5 ≤ 3

Key Concepts

Inequalities

Linear Functions

Solving for x

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