Worksheet for solving one-step equations using multiplication and division.

Problem: Solve the one-step equations involving multiplication and division.

The goal is to isolate the variable \( x \) in each equation. Let's solve each equation step by step.

---

#### Equation 1: \( 3x = 18 \)

To solve for \( x \), divide both sides of the equation by 3:
\[
3x = 18
\]
\[
x = \frac{18}{3}
\]
\[
x = 6
\]

Solution: \( x = 6 \)

---

#### Equation 2: \( 3x = 15 \)

To solve for \( x \), divide both sides of the equation by 3:
\[
3x = 15
\]
\[
x = \frac{15}{3}
\]
\[
x = 5
\]

Solution: \( x = 5 \)

---

#### Equation 3: \( 3x = 5 \)

To solve for \( x \), divide both sides of the equation by 3:
\[
3x = 5
\]
\[
x = \frac{5}{3}
\]

Solution: \( x = \frac{5}{3} \)

---

#### Equation 4: \( \frac{x}{3} = 5 \)

To solve for \( x \), multiply both sides of the equation by 3:
\[
\frac{x}{3} = 5
\]
\[
x = 5 \cdot 3
\]
\[
x = 15
\]

Solution: \( x = 15 \)

---

#### Equation 5: \( 5 = \frac{x}{3} \)

This is the same as \( \frac{x}{3} = 5 \). To solve for \( x \), multiply both sides of the equation by 3:
\[
5 = \frac{x}{3}
\]
\[
x = 5 \cdot 3
\]
\[
x = 15
\]

Solution: \( x = 15 \)

---

#### Equation 8: \( -15 = -\frac{x}{3} \)

To solve for \( x \), first eliminate the negative sign by multiplying both sides by \(-1\):
\[
-15 = -\frac{x}{3}
\]
\[
15 = \frac{x}{3}
\]

Now, multiply both sides by 3:
\[
15 = \frac{x}{3}
\]
\[
x = 15 \cdot 3
\]
\[
x = 45
\]

Solution: \( x = 45 \)

---

#### Equation 9: \( -15 = -3x \)

To solve for \( x \), first eliminate the negative sign by dividing both sides by \(-3\):
\[
-15 = -3x
\]
\[
x = \frac{-15}{-3}
\]
\[
x = 5
\]

Solution: \( x = 5 \)

---

#### Equation 10: \( -15 = 3x \)

To solve for \( x \), divide both sides of the equation by 3:
\[
-15 = 3x
\]
\[
x = \frac{-15}{3}
\]
\[
x = -5
\]

Solution: \( x = -5 \)

---

#### Equation 11: \( -15 = 2x \)

To solve for \( x \), divide both sides of the equation by 2:
\[
-15 = 2x
\]
\[
x = \frac{-15}{2}
\]
\[
x = -\frac{15}{2}
\]

Solution: \( x = -\frac{15}{2} \)

---

#### Equation 12: \( -15 = 4x \)

To solve for \( x \), divide both sides of the equation by 4:
\[
-15 = 4x
\]
\[
x = \frac{-15}{4}
\]

Solution: \( x = -\frac{15}{4} \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ x = 6 \\
2. & \ x = 5 \\
3. & \ x = \frac{5}{3} \\
4. & \ x = 15 \\
5. & \ x = 15 \\
8. & \ x = 45 \\
9. & \ x = 5 \\
10. & \ x = -5 \\
11. & \ x = -\frac{15}{2} \\
12. & \ x = -\frac{15}{4}
\end{aligned}
}
\]