LITERAL EQUATIONS WORKSHEET Solve for the indicated ... - Free Printable

Let's solve each of these literal equations for the indicated variable. A literal equation is an equation that involves multiple variables, and we are solving for one specific variable in terms of the others.

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1) $ P = IRT $ (solve for $ T $)

Divide both sides by $ IR $:
$$
T = \frac{P}{IR}
$$

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2) $ A = 2(L + W) $ (solve for $ W $)

Divide both sides by 2:
$$
\frac{A}{2} = L + W
$$
Subtract $ L $:
$$
W = \frac{A}{2} - L
$$

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3) $ y = 5x - 6 $ (solve for $ x $)

Add 6 to both sides:
$$
y + 6 = 5x
$$
Divide by 5:
$$
x = \frac{y + 6}{5}
$$

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4) $ 2x - 3y = 8 $ (solve for $ y $)

Subtract $ 2x $:
$$
-3y = 8 - 2x
$$
Divide by $-3$:
$$
y = \frac{2x - 8}{3}
$$

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5) $ \frac{x + y}{3} = 5 $ (solve for $ x $)

Multiply both sides by 3:
$$
x + y = 15
$$
Subtract $ y $:
$$
x = 15 - y
$$

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6) $ y = mx + b $ (solve for $ b $)

Subtract $ mx $:
$$
b = y - mx
$$

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7) $ ax + by = c $ (solve for $ y $)

Subtract $ ax $:
$$
by = c - ax
$$
Divide by $ b $:
$$
y = \frac{c - ax}{b}
$$

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8) $ A = 1.2h(b + c) $ (solve for $ b $)

Divide both sides by $ 1.2h $:
$$
\frac{A}{1.2h} = b + c
$$
Subtract $ c $:
$$
b = \frac{A}{1.2h} - c
$$

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9) $ V = LWH $ (solve for $ L $)

Divide both sides by $ WH $:
$$
L = \frac{V}{WH}
$$

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10) $ A = 4\pi r^2 $ (solve for $ r^2 $)

Divide by $ 4\pi $:
$$
r^2 = \frac{A}{4\pi}
$$

> Note: If you want $ r $, take square root: $ r = \sqrt{\frac{A}{4\pi}} $, but since it asks for $ r^2 $, this is sufficient.

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11) $ V = \pi r^2 h $ (solve for $ h $)

Divide by $ \pi r^2 $:
$$
h = \frac{V}{\pi r^2}
$$

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12) $ 7x - y = 14 $ (solve for $ x $)

Add $ y $:
$$
7x = 14 + y
$$
Divide by 7:
$$
x = \frac{14 + y}{7}
$$

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13) $ A = \frac{x + y}{2} $ (solve for $ y $)

Multiply both sides by 2:
$$
2A = x + y
$$
Subtract $ x $:
$$
y = 2A - x
$$

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14) $ R = \frac{E}{I} $ (solve for $ I $)

Multiply both sides by $ I $:
$$
RI = E
$$
Divide by $ R $:
$$
I = \frac{E}{R}
$$

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15) $ x = \frac{yz}{6} $ (solve for $ z $)

Multiply both sides by 6:
$$
6x = yz
$$
Divide by $ y $:
$$
z = \frac{6x}{y}
$$

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16) $ A = \frac{FL}{2L} $ (solve for $ L $)

Simplify right-hand side:
$$
A = \frac{F}{2}
$$
Wait — this simplifies to a constant unless $ L $ cancels out.

But let’s look:
$$
A = \frac{FL}{2L} = \frac{F}{2}, \quad \text{(if } L \neq 0\text{)}
$$
So $ A = \frac{F}{2} $, which means $ L $ cancels out — so $ A $ does not depend on $ L $.

This suggests either:
- There's a typo, or
- The equation is meant to be $ A = \frac{FL}{2} $, then solve for $ L $

But as written: $ A = \frac{FL}{2L} = \frac{F}{2} $, so $ A $ is independent of $ L $ → no unique solution for $ L $ unless more info.

But if we assume it's $ A = \frac{FL}{2} $, then:

$$
L = \frac{2A}{F}
$$

But based on what's written:
$$
A = \frac{FL}{2L} = \frac{F}{2} \Rightarrow \text{No dependence on } L
$$

So unless $ L $ is canceled, we cannot solve for $ L $. So perhaps it's a typo.

Alternatively, maybe it's $ A = \frac{FL}{2} $ → then:

$$
L = \frac{2A}{F}
$$

We’ll go with that interpretation (common in physics). So:
$$
\boxed{L = \frac{2A}{F}}
$$

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17) $ A = \frac{a + b + c}{3} $ (solve for $ b $)

Multiply by 3:
$$
3A = a + b + c
$$
Subtract $ a $ and $ c $:
$$
b = 3A - a - c
$$

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18) $ 12x - 4y = 20 $ (solve for $ y $)

Subtract $ 12x $:
$$
-4y = 20 - 12x
$$
Divide by $-4$:
$$
y = \frac{12x - 20}{4} = 3x - 5
$$

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19) $ x = \frac{2y - z}{4} $ (solve for $ z $)

Multiply both sides by 4:
$$
4x = 2y - z
$$
Subtract $ 2y $:
$$
4x - 2y = -z
$$
Multiply by $-1$:
$$
z = 2y - 4x
$$

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20) $ P = \frac{R - C}{N} $ (solve for $ R $)

Multiply both sides by $ N $:
$$
PN = R - C
$$
Add $ C $:
$$
R = PN + C
$$

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✔ Final Answers:

1) $ T = \frac{P}{IR} $
2) $ W = \frac{A}{2} - L $
3) $ x = \frac{y + 6}{5} $
4) $ y = \frac{2x - 8}{3} $
5) $ x = 15 - y $
6) $ b = y - mx $
7) $ y = \frac{c - ax}{b} $
8) $ b = \frac{A}{1.2h} - c $
9) $ L = \frac{V}{WH} $
10) $ r^2 = \frac{A}{4\pi} $
11) $ h = \frac{V}{\pi r^2} $
12) $ x = \frac{14 + y}{7} $
13) $ y = 2A - x $
14) $ I = \frac{E}{R} $
15) $ z = \frac{6x}{y} $
16) $ L = \frac{2A}{F} $ *(assuming typo; otherwise no solution)*
17) $ b = 3A - a - c $
18) $ y = 3x - 5 $
19) $ z = 2y - 4x $
20) $ R = PN + C $

Let me know if you'd like these formatted in a table or explained further!