Worksheet Solving Literal Equations Worksheet - Free Printable

Worksheet: Solving Literal Equations

The task is to solve each equation for the indicated variable. Below are the solutions with step-by-step explanations.

---

#### 1. \( V = Bh \); for \( B \)
- Start with the equation: \( V = Bh \)
- To solve for \( B \), divide both sides by \( h \):
\[
B = \frac{V}{h}
\]

Answer: \( B = \frac{V}{h} \)

---

#### 2. \( d = \frac{c}{r} \); for \( c \)
- Start with the equation: \( d = \frac{c}{r} \)
- To solve for \( c \), multiply both sides by \( r \):
\[
c = dr
\]

Answer: \( c = dr \)

---

#### 3. \( L = \frac{A}{W} \); for \( W \)
- Start with the equation: \( L = \frac{A}{W} \)
- To solve for \( W \), multiply both sides by \( W \) and then divide by \( L \):
\[
LW = A \implies W = \frac{A}{L}
\]

Answer: \( W = \frac{A}{L} \)

---

#### 4. \( x = \frac{1}{2} r^2 w \); for \( w \)
- Start with the equation: \( x = \frac{1}{2} r^2 w \)
- To solve for \( w \), multiply both sides by 2 and then divide by \( r^2 \):
\[
2x = r^2 w \implies w = \frac{2x}{r^2}
\]

Answer: \( w = \frac{2x}{r^2} \)

---

#### 5. \( V = \frac{b^2 h}{3} \); for \( h \)
- Start with the equation: \( V = \frac{b^2 h}{3} \)
- To solve for \( h \), multiply both sides by 3 and then divide by \( b^2 \):
\[
3V = b^2 h \implies h = \frac{3V}{b^2}
\]

Answer: \( h = \frac{3V}{b^2} \)

---

#### 6. \( F = \frac{k E_1 E_2}{d^2} \); for \( E_1 \)
- Start with the equation: \( F = \frac{k E_1 E_2}{d^2} \)
- To solve for \( E_1 \), multiply both sides by \( d^2 \) and then divide by \( k E_2 \):
\[
F d^2 = k E_1 E_2 \implies E_1 = \frac{F d^2}{k E_2}
\]

Answer: \( E_1 = \frac{F d^2}{k E_2} \)

---

#### 7. \( 3w = \frac{1}{2} z - 5 \); for \( z \)
- Start with the equation: \( 3w = \frac{1}{2} z - 5 \)
- Add 5 to both sides:
\[
3w + 5 = \frac{1}{2} z
\]
- Multiply both sides by 2 to solve for \( z \):
\[
z = 2(3w + 5) = 6w + 10
\]

Answer: \( z = 6w + 10 \)

---

#### 8. \( 5ax - 2b = cx - c \); for \( b \)
- Start with the equation: \( 5ax - 2b = cx - c \)
- Isolate the term involving \( b \) by moving all other terms to the other side:
\[
-2b = cx - c - 5ax
\]
- Factor out \( x \) on the right-hand side:
\[
-2b = x(c - 5a) - c
\]
- Divide both sides by \(-2\) to solve for \( b \):
\[
b = \frac{c - x(c - 5a)}{2}
\]

Answer: \( b = \frac{c - x(c - 5a)}{2} \)

---

#### 9. \( 3x + a = b \); for \( x \)
- Start with the equation: \( 3x + a = b \)
- Subtract \( a \) from both sides:
\[
3x = b - a
\]
- Divide both sides by 3:
\[
x = \frac{b - a}{3}
\]

Answer: \( x = \frac{b - a}{3} \)

---

#### 10. \( v = V + gt \); for \( t \)
- Start with the equation: \( v = V + gt \)
- Subtract \( V \) from both sides:
\[
v - V = gt
\]
- Divide both sides by \( g \):
\[
t = \frac{v - V}{g}
\]

Answer: \( t = \frac{v - V}{g} \)

---

#### 11. \( S = P + prt \); for \( r \)
- Start with the equation: \( S = P + prt \)
- Subtract \( P \) from both sides:
\[
S - P = prt
\]
- Divide both sides by \( pt \):
\[
r = \frac{S - P}{pt}
\]

Answer: \( r = \frac{S - P}{pt} \)

---

#### 12. \( A = \frac{1}{2} h(b + c) \); for \( c \)
- Start with the equation: \( A = \frac{1}{2} h(b + c) \)
- Multiply both sides by 2 to eliminate the fraction:
\[
2A = h(b + c)
\]
- Divide both sides by \( h \):
\[
\frac{2A}{h} = b + c
\]
- Subtract \( b \) from both sides to solve for \( c \):
\[
c = \frac{2A}{h} - b
\]

Answer: \( c = \frac{2A}{h} - b \)

---

#### 13. \( F = \frac{9}{5} C + 32 \); for \( C \)
- Start with the equation: \( F = \frac{9}{5} C + 32 \)
- Subtract 32 from both sides:
\[
F - 32 = \frac{9}{5} C
\]
- Multiply both sides by \( \frac{5}{9} \) to solve for \( C \):
\[
C = \frac{5}{9}(F - 32)
\]

Answer: \( C = \frac{5}{9}(F - 32) \)

---

#### 14. \( \frac{am - bn}{c} = d \); for \( m \)
- Start with the equation: \( \frac{am - bn}{c} = d \)
- Multiply both sides by \( c \) to eliminate the denominator:
\[
am - bn = cd
\]
- Add \( bn \) to both sides:
\[
am = cd + bn
\]
- Divide both sides by \( a \) to solve for \( m \):
\[
m = \frac{cd + bn}{a}
\]

Answer: \( m = \frac{cd + bn}{a} \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \quad B = \frac{V}{h} \\
2. & \quad c = dr \\
3. & \quad W = \frac{A}{L} \\
4. & \quad w = \frac{2x}{r^2} \\
5. & \quad h = \frac{3V}{b^2} \\
6. & \quad E_1 = \frac{F d^2}{k E_2} \\
7. & \quad z = 6w + 10 \\
8. & \quad b = \frac{c - x(c - 5a)}{2} \\
9. & \quad x = \frac{b - a}{3} \\
10. & \quad t = \frac{v - V}{g} \\
11. & \quad r = \frac{S - P}{pt} \\
12. & \quad c = \frac{2A}{h} - b \\
13. & \quad C = \frac{5}{9}(F - 32) \\
14. & \quad m = \frac{cd + bn}{a}
\end{aligned}
}
\]