Is (1,1) a solution to the inquality 2x+18y<20?

To check whether \((1,1)\) is a solution to the inequality \(2x + 18y < 20\), we substitute \(x = 1\) and \(y = 1\) into the inequality:

\[
2(1) + 18(1) < 20
\]

\[
2 + 18 < 20
\]

\[
20 < 20
\]

This statement is false because \(20\) is not less than \(20\); it is equal to \(20\). Therefore, \((1,1)\) is **not** a solution to the inequality \(2x + 18y < 20\).

Would you like a more detailed explanation or have any questions?

Here are 5 related questions to consider:
1. How do you determine whether a point satisfies an inequality?
2. What is the graphical representation of \(2x + 18y < 20\)?
3. How do you solve and graph linear inequalities in two variables?
4. What is the difference between strict inequalities (\(<\)) and non-strict inequalities (\(\leq\))?
5. How do boundary lines affect the solution set of an inequality?

**Tip:** Always check the strictness of the inequality when verifying whether a point is a solution.

Is (1,1) a solution to the inequality 2x + 18y < 20?

Learn how to determine whether the point (1,1) satisfies the inequality 2x + 18y < 20 by substituting the values of x and y. Understand key concepts in linear inequalities, suitable for students in Grades 6-8.

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