Pre-Algebra worksheet for solving equations with variables.

Problem Description:

The image contains a worksheet titled "Pre Algebra: Solve for Each Variable." It consists of 15 equations, and the task is to solve each equation for the variable.

Solution Approach:

To solve each equation, we will isolate the variable on one side of the equation using algebraic operations such as addition, subtraction, multiplication, or division. Let's solve each equation step by step.

---

Equation 1: \( 16 = 9 + s \)

1. Subtract 9 from both sides:
\[
16 - 9 = s
\]
2. Simplify:
\[
s = 7
\]

Answer: \( s = 7 \)

---

Equation 2: \( x + 7 = 5 \)

1. Subtract 7 from both sides:
\[
x = 5 - 7
\]
2. Simplify:
\[
x = -2
\]

Answer: \( x = -2 \)

---

Equation 3: \( 27 = 6x \)

1. Divide both sides by 6:
\[
x = \frac{27}{6}
\]
2. Simplify:
\[
x = 4.5
\]

Answer: \( x = 4.5 \)

---

Equation 4: \( x - 5 = 1 \)

1. Add 5 to both sides:
\[
x = 1 + 5
\]
2. Simplify:
\[
x = 6
\]

Answer: \( x = 6 \)

---

Equation 5: \( 3 = 2 + y \)

1. Subtract 2 from both sides:
\[
y = 3 - 2
\]
2. Simplify:
\[
y = 1
\]

Answer: \( y = 1 \)

---

Equation 6: \( 8y + 5 = 23 \)

1. Subtract 5 from both sides:
\[
8y = 23 - 5
\]
2. Simplify:
\[
8y = 18
\]
3. Divide both sides by 8:
\[
y = \frac{18}{8}
\]
4. Simplify:
\[
y = 2.25
\]

Answer: \( y = 2.25 \)

---

Equation 7: \( x + 9 = 13 \)

1. Subtract 9 from both sides:
\[
x = 13 - 9
\]
2. Simplify:
\[
x = 4
\]

Answer: \( x = 4 \)

---

Equation 8: \( x \div 5 = 12 \)

1. Multiply both sides by 5:
\[
x = 12 \times 5
\]
2. Simplify:
\[
x = 60
\]

Answer: \( x = 60 \)

---

Equation 9: \( 73 = 1 + 8y \)

1. Subtract 1 from both sides:
\[
72 = 8y
\]
2. Divide both sides by 8:
\[
y = \frac{72}{8}
\]
3. Simplify:
\[
y = 9
\]

Answer: \( y = 9 \)

---

Equation 10: \( 4 = 3 + x \)

1. Subtract 3 from both sides:
\[
x = 4 - 3
\]
2. Simplify:
\[
x = 1
\]

Answer: \( x = 1 \)

---

Equation 11: \( 8 = 9 - x \)

1. Subtract 9 from both sides:
\[
8 - 9 = -x
\]
2. Simplify:
\[
-1 = -x
\]
3. Multiply both sides by -1:
\[
x = 1
\]

Answer: \( x = 1 \)

---

Equation 12: \( 6 = y - 6 \)

1. Add 6 to both sides:
\[
y = 6 + 6
\]
2. Simplify:
\[
y = 12
\]

Answer: \( y = 12 \)

---

Equation 13: \( 63 = x \times 7 \)

1. Divide both sides by 7:
\[
x = \frac{63}{7}
\]
2. Simplify:
\[
x = 9
\]

Answer: \( x = 9 \)

---

Equation 14: \( 1 = 6y + 13 \)

1. Subtract 13 from both sides:
\[
1 - 13 = 6y
\]
2. Simplify:
\[
-12 = 6y
\]
3. Divide both sides by 6:
\[
y = \frac{-12}{6}
\]
4. Simplify:
\[
y = -2
\]

Answer: \( y = -2 \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ s = 7 \\
2. & \ x = -2 \\
3. & \ x = 4.5 \\
4. & \ x = 6 \\
5. & \ y = 1 \\
6. & \ y = 2.25 \\
7. & \ x = 4 \\
8. & \ x = 60 \\
9. & \ y = 9 \\
10. & \ x = 1 \\
11. & \ x = 1 \\
12. & \ y = 12 \\
13. & \ x = 9 \\
14. & \ y = -2 \\
\end{aligned}
}
\]