Math Snap

STEP 1

1. We are given the inequality $2x + 5y < 24$.
2. We need to determine which point among the given options satisfies the inequality.

STEP 2

1. Substitute each point into the inequality.
2. Check if the inequality holds true for each point.
3. Identify the point(s) that satisfy the inequality.

STEP 3

Substitute point $A(7,2)$ into the inequality $2x + 5y < 24$.
$$2(7) + 5(2) = 14 + 10 = 24$$

STEP 4

Check if the inequality holds for point $A(7,2)$.
Since $24 \not< 24$, point $A(7,2)$ does not satisfy the inequality.

STEP 5

Substitute point $B(2,7)$ into the inequality $2x + 5y < 24$.
$$2(2) + 5(7) = 4 + 35 = 39$$

STEP 6

Check if the inequality holds for point $B(2,7)$.
Since $39 \not< 24$, point $B(2,7)$ does not satisfy the inequality.

STEP 7

Substitute point $C(-3,5)$ into the inequality $2x + 5y < 24$.
$$2(-3) + 5(5) = -6 + 25 = 19$$

STEP 8

Check if the inequality holds for point $C(-3,5)$.
Since $19 < 24$, point $C(-3,5)$ satisfies the inequality.

STEP 9

Substitute point $D(5,3)$ into the inequality $2x + 5y < 24$.
$$2(5) + 5(3) = 10 + 15 = 25$$

Check if the inequality holds for point $D(5,3)$.
Since $25 \not< 24$, point $D(5,3)$ does not satisfy the inequality.
The point that satisfies the inequality is:
$\boxed{C(-3,5)}$