To determine if the point [tex]\((15, 5)\)[/tex] satisfies the inequality [tex]\(3x - 4y \geq 24\)[/tex], we need to substitute [tex]\(x = 15\)[/tex] and [tex]\(y = 5\)[/tex] into the inequality and check if the resulting expression holds true.
1. Substitute:
[tex]\[
3x - 4y \geq 24
\][/tex]
We substitute [tex]\(x = 15\)[/tex] and [tex]\(y = 5\)[/tex]:
[tex]\[
3(15) - 4(5) \geq 24
\][/tex]
2. Calculate:
We calculate the left-hand side of the inequality:
[tex]\[
3(15) = 45
\][/tex]
[tex]\[
4(5) = 20
\][/tex]
Thus, the expression becomes:
[tex]\[
45 - 20 \geq 24
\][/tex]
3. Simplify:
Simplify the left-hand side:
[tex]\[
25 \geq 24
\][/tex]
4. Interpret the result:
Since [tex]\(25 \geq 24\)[/tex] is a true statement, the given point [tex]\((15, 5)\)[/tex] satisfies the inequality.
Therefore, the student is correct. The point [tex]\((15, 5)\)[/tex] is indeed a solution to the inequality [tex]\(3x - 4y \geq 24\)[/tex].
