To determine whether the point [tex]\((1, -1)\)[/tex] satisfies the inequality [tex]\(40x - 22y \leq 50\)[/tex], we can follow these steps:
1. Substitute the coordinates of the point into the inequality:
Given the point [tex]\((x, y) = (1, -1)\)[/tex], substitute [tex]\(x = 1\)[/tex] and [tex]\(y = -1\)[/tex] into the inequality:
[tex]\[
40(1) - 22(-1) \leq 50
\][/tex]
2. Simplify the left-hand side of the inequality:
Calculate the expression:
[tex]\[
40(1) - 22(-1) = 40 + 22
\][/tex]
The two negatives in [tex]\(-22(-1)\)[/tex] cancel each other out, resulting in:
[tex]\[
40 + 22 = 62
\][/tex]
3. Compare the simplified inequality:
Now we need to compare [tex]\(62\)[/tex] with the right-hand side of the inequality:
[tex]\[
62 \leq 50
\][/tex]
4. Evaluate the truth of the statement:
Clearly, [tex]\(62\)[/tex] is not less than or equal to [tex]\(50\)[/tex]. Therefore, the inequality [tex]\(40x - 22y \leq 50\)[/tex] is not satisfied by the point [tex]\((1, -1)\)[/tex].
Conclusion: The statement that the point [tex]\((1, -1)\)[/tex] satisfies the inequality [tex]\(40x - 22y \leq 50\)[/tex] is False.
