Does the point (4,4) satisfy the inequality 2x+2y<18?

To check if the point \((4, 4)\) satisfies the inequality \(2x + 2y < 18\), we substitute \(x = 4\) and \(y = 4\) into the inequality.

\[
2(4) + 2(4) < 18
\]

Simplifying:

\[
8 + 8 < 18
\]

\[
16 < 18
\]

Since \(16 < 18\) is true, the point \((4, 4)\) does satisfy the inequality \(2x + 2y < 18\).

Would you like further details or have any questions?

Here are 5 related questions:
1. What does the solution set of this inequality look like graphically?
2. How would the inequality change if the sign was \( \leq \) instead of \( < \)?
3. What happens if the point was \( (5, 5) \)? Does it satisfy the inequality?
4. Can you express the inequality \( 2x + 2y < 18 \) in slope-intercept form?
5. How would this inequality change if the boundary line was shifted?

**Tip:** To solve inequalities, always substitute the values and simplify step-by-step to check if the inequality holds.

Check if the point (4,4) satisfies the inequality 2x + 2y < 18 by substituting the values and simplifying the expression. This problem covers key algebraic concepts such as inequalities and linear equations, suitable for students in Grades 6-8.

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