Question

solve the linear inequality by graphing. graph the inequality on your recording sheet. determine whether the ordered pair is a solution. 2x - 3y < 6

Explanation:

Step1: Test (-5, -3) in inequality

Substitute $x=-5, y=-3$:
$2(-5) - 3(-3) = -10 + 9 = -1$
$-1 < 6$, so it is a solution.

Step2: Test (-4, 2) in inequality

Substitute $x=-4, y=2$:
$2(-4) - 3(2) = -8 - 6 = -14$
$-14 < 6$, so it is a solution.

Step3: Test (-3, -3) in inequality

Substitute $x=-3, y=-3$:
$2(-3) - 3(-3) = -6 + 9 = 3$
$3 < 6$, so it is a solution.

Step4: Test (0, 0) in inequality

Substitute $x=0, y=0$:
$2(0) - 3(0) = 0$
$0 < 6$, so it is a solution.

Step5: Test (3, 0) in inequality

Substitute $x=3, y=0$:
$2(3) - 3(0) = 6$
$6
less 6$, so it is not a solution.

Step6: Test (4, 5) in inequality

Substitute $x=4, y=5$:
$2(4) - 3(5) = 8 - 15 = -7$
$-7 < 6$, so it is a solution.

Step7: Test (7, -4) in inequality

Substitute $x=7, y=-4$:
$2(7) - 3(-4) = 14 + 12 = 26$
$26
less 6$, so it is not a solution.

Step8: Test (-6, -6) in inequality

Substitute $x=-6, y=-6$:
$2(-6) - 3(-6) = -12 + 18 = 6$
$6
less 6$, so it is not a solution.

Answer:

SOLUTIONS:

(-5, -3), (-4, 2), (-3, -3), (0, 0), (4, 5)

NOT SOLUTIONS:

(3, 0), (7, -4), (-6, -6)