Multi-step equations activity - Free Printable

Let's solve each of the multi-step equations step by step.

---

1) \( 2a - 6 = 4 \)

#### Step 1: Add 6 to both sides to isolate the term with \( a \).
\[
2a - 6 + 6 = 4 + 6
\]
\[
2a = 10
\]

#### Step 2: Divide both sides by 2 to solve for \( a \).
\[
\frac{2a}{2} = \frac{10}{2}
\]
\[
a = 5
\]

#### Final Answer:
\[
\boxed{5}
\]

---

2) \( \frac{n+1}{-2} = 15 \)

#### Step 1: Eliminate the denominator by multiplying both sides by \(-2\).
\[
-2 \cdot \frac{n+1}{-2} = 15 \cdot (-2)
\]
\[
n + 1 = -30
\]

#### Step 2: Subtract 1 from both sides to isolate \( n \).
\[
n + 1 - 1 = -30 - 1
\]
\[
n = -31
\]

#### Final Answer:
\[
\boxed{-31}
\]

---

3) \( 9x + 27 = -72 \)

#### Step 1: Subtract 27 from both sides to isolate the term with \( x \).
\[
9x + 27 - 27 = -72 - 27
\]
\[
9x = -99
\]

#### Step 2: Divide both sides by 9 to solve for \( x \).
\[
\frac{9x}{9} = \frac{-99}{9}
\]
\[
x = -11
\]

#### Final Answer:
\[
\boxed{-11}
\]

---

4) \( \frac{y}{5} - 6 = 8 \)

#### Step 1: Add 6 to both sides to isolate the term with \( y \).
\[
\frac{y}{5} - 6 + 6 = 8 + 6
\]
\[
\frac{y}{5} = 14
\]

#### Step 2: Multiply both sides by 5 to solve for \( y \).
\[
5 \cdot \frac{y}{5} = 14 \cdot 5
\]
\[
y = 70
\]

#### Final Answer:
\[
\boxed{70}
\]

---

Summary of Answers:

1. \( a = 5 \)
2. \( n = -31 \)
3. \( x = -11 \)
4. \( y = 70 \)

\[
\boxed{5, -31, -11, 70}
\]