Question

Solve the inequality.
1. 6n - 3 > -18
2. 6 - 3p greater than or equal to -9
3. -4 less than or equal to 4(6y -12) -2y

Answer 1

Let's solve each inequality one by one.

### 1. Solve the inequality \( 6n - 3 > -18 \)

**Step 1:** Add 3 to both sides.

\[
6n - 3 + 3 > -18 + 3
\]
\[
6n > -15
\]

**Step 2:** Divide both sides by 6.

\[
n > -\frac{15}{6}
\]

**Step 3:** Simplify the fraction.

\[
n > -\frac{5}{2} \quad \text{or} \quad n > -2.5
\]

### 2. Solve the inequality \( 6 - 3p \geq -9 \)

**Step 1:** Subtract 6 from both sides.

\[
6 - 6 - 3p \geq -9 - 6
\]
\[
-3p \geq -15
\]

**Step 2:** Divide both sides by -3 (note that this reverses the inequality).

\[
p \leq 5
\]

### 3. Solve the inequality \( -4 \leq 4(6y - 12) - 2y \)

**Step 1:** Expand the left side.

\[
-4 \leq 24y - 48 - 2y
\]

**Step 2:** Combine like terms.

\[
-4 \leq (24y - 2y) - 48
\]
\[
-4 \leq 22y - 48
\]

**Step 3:** Add 48 to both sides.

\[
-4 + 48 \leq 22y
\]
\[
44 \leq 22y
\]

**Step 4:** Divide both sides by 22.

\[
2 \leq y \quad \text{or} \quad y \geq 2
\]

### Summary of solutions:

1. \( n > -2.5 \)
2. \( p \leq 5 \)
3. \( y \geq 2 \)