Question

solve the inequality:
-3y + 12 > 21
a
( y < -3 )
b
( y > -3 )
c
( y < -11 )
d
( y > -11 )

Explanation:

Step1: Subtract 12 from both sides

To isolate the term with \( y \), we subtract 12 from both sides of the inequality \( -3y + 12>21 \). This gives us \( -3y+12 - 12>21 - 12 \), which simplifies to \( -3y>9 \).

Step2: Divide by - 3 and reverse inequality

When we divide both sides of an inequality by a negative number, the direction of the inequality sign reverses. So, dividing both sides of \( -3y > 9 \) by - 3, we get \( y < - 3 \)? Wait, no, wait, let's check again. Wait, the original inequality is \( - 3y+12>21 \). Subtract 12: \( - 3y>21 - 12=9 \). Then divide by - 3: \( y <\frac{9}{-3}=- 3 \). Wait, but the options are A: \( y < - 3 \), B: \( y > - 3 \), C: \( y < - 11 \), D: \( y > - 11 \). Wait, maybe I misread the original inequality. Wait, maybe the original inequality is \( - 3y+12>21 \)? Wait, no, maybe it's \( - 3y + 12>21 \), or maybe \( - 3y+12>21 \). Wait, let's do the steps again.

1. Start with \( - 3y+12>21 \)
2. Subtract 12 from both sides: \( - 3y>21 - 12 \)

\( - 3y>9 \)

1. Divide both sides by - 3. Remember, when dividing by a negative number, the inequality sign flips.

\( y <\frac{9}{-3}\)
\( y < - 3 \)

So the solution is \( y < - 3 \), which is option A. Wait, but let's check the options again. Option A is \( y < - 3 \), option B is \( y > - 3 \), option C is \( y < - 11 \), option D is \( y > - 11 \). So the correct answer is A.

Wait, maybe I made a mistake in the sign. Let's verify with a test value. Let's take \( y=-4 \) (which is less than - 3). Plug into \( - 3y + 12 \): \( - 3\times(-4)+12 = 12 + 12=24 \), and 24>21, which is true. Now take \( y = - 2 \) (which is greater than - 3). Plug into \( - 3y+12 \): \( - 3\times(-2)+12=6 + 12 = 18 \), and 18>21? No, 18<21. So when \( y > - 3 \), the inequality does not hold. When \( y < - 3 \), it holds. So the solution is \( y < - 3 \), which is option A.

Answer:

A. \( y < - 3 \)