Answer:
Explanation:
To solve the inequality -2(x + 6) < 3(x + 1), let's go step by step:
1. Start by applying the distributive property to both sides of the inequality:
-2(x + 6) < 3(x + 1)
-2x - 12 < 3x + 3
Justification: We distribute -2 to both x and 6 on the left side, and 3 to both x and 1 on the right side.
2. Next, combine like terms on both sides of the inequality:
-2x - 12 < 3x + 3
Justification: We group the x terms and the constant terms separately on each side of the inequality.
3. To isolate the variable, let's get rid of the 3x term on the right side by subtracting 3x from both sides:
-2x - 12 - 3x < 3x + 3 - 3x
-5x - 12 < 3
Justification: We subtract 3x from both sides to eliminate the 3x term on the right side.
4. Now, let's isolate the x term by adding 12 to both sides of the inequality:
-5x - 12 + 12 < 3 + 12
-5x < 15
Justification: We add 12 to both sides to eliminate the constant term -12 on the left side.
5. Finally, to solve for x, we divide both sides of the inequality by -5. Remember that when dividing by a negative number, we need to reverse the inequality symbol:
(-5x) / -5 > 15 / -5
x > -3
Justification: We divide both sides of the inequality by -5 to isolate the x term.
Therefore, the correct justification for each step is as follows:
1. Distributive Property
2. Combine Like Terms
3. Addition Property of Order
4. Addition Property of Order
5. Division Property of Order
I hope this clarifies the steps taken to solve the inequality. If you have any further questions, feel free to ask!