Does the point (2,1) satisfy the inequality 2x+14y>18?

To check if the point \((2,1)\) satisfies the inequality \(2x + 14y > 18\), substitute \(x = 2\) and \(y = 1\) into the inequality:

\[
2(2) + 14(1) > 18
\]

Simplifying the left-hand side:

\[
4 + 14 > 18
\]

\[
18 > 18
\]

Since \(18\) is **not greater than** \(18\), the inequality is **not satisfied**. Therefore, the point \((2, 1)\) does **not** satisfy the inequality \(2x + 14y > 18\).

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How can we determine whether a point satisfies any inequality in general?
2. What does the solution set of the inequality \(2x + 14y > 18\) represent graphically?
3. What would happen if the inequality were \(2x + 14y \geq 18\)?
4. How do we graph the inequality \(2x + 14y > 18\) on a coordinate plane?
5. Can we solve and describe the region where \(2x + 14y > 18\) holds?

**Tip:** Always check whether the inequality symbol includes equality (≥ or ≤) before making conclusions about boundary points.

Does the point (2,1) satisfy the inequality 2x + 14y > 18?

Explore how to determine if the point (2,1) satisfies the inequality 2x + 14y > 18. This step-by-step solution explains the process of substituting values into the inequality and simplifying. Suitable for students in Grades 7-8 learning about linear inequalities.

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