Final answer:
To solve the inequalities -3x - 7 < 11 and 4y + 3 > 1, both inequalities are first solved individually for x and y. The Transitive Property could be applied if there was a third inequality relating y to x, allowing us to find a solution that satisfies all three.
Step-by-step explanation:
The question involves solving two inequalities: -3x - 7 < 11 and 4y + 3 > 1. First, we will solve each inequality for x and y respectively, then we will use the Transitive Property to combine them.
Step 1: Solve the inequalities
For the first inequality:
-3x - 7 < 11
We add 7 to both sides:
-3x < 18
Now, we divide both sides by -3 (remember that dividing by a negative number reverses the inequality):
x > -6
For the second inequality:
4y + 3 > 1
We subtract 3 from both sides:
4y > -2
We divide both sides by 4:
y > -0.5
Step 2: Apply the Transitive Property
The Transitive Property of inequalities states that if a > b and b > c, then a > c. However, to use this property, we need to have the same inequality symbol in both of our inequalities. Since our target is to keep the leading coefficient positive, we do not need to make further changes as both inequalities already satisfy this condition.
Step 3: Solve using the Transitive Property
We cannot directly apply the Transitive Property as the inequalities are with different variables. However, If there were a third inequality that related y to x, then we could use the property to find a solution that satisfies all three inequalities.