Before you read

Answer first — see what you already know.

The area of a rectangular banner is given by $A = bh$ . A designer knows the area $A$ and base $b$ , and needs to find the height $h$ . Which expression gives $h$ in terms of $A$ and $b$ ?

A
$h = A - b$
B
$h = \frac{A}{b}$
C
$h = A b$
D
$h = \frac{b}{A}$

Check your answer

Answer:

Before you read

Answer first — see what you already know.

A running track's circumference is $C = 2 π r$ . A coach measures the circumference and needs to find the radius. Which equation gives $r$ in terms of $C$ ?

A
$r = C - 2 π$
B
$r = \frac{2 π}{C}$
C
$r = \frac{C}{2 π}$
D
$r = 2 π C$

Check your answer

Answer:

Theory

What Is a Literal Equation?

A literal equation is an equation with two or more variables. Instead of solving for a number, you solve for one variable in terms of the others.

You already know many literal equations — they're just formulas:
- Area of a rectangle: $A = lw$
- Distance formula: $d = rt$
- Slope-intercept form: $y = mx + b$
- Temperature conversion: $F = \frac{9}{5}C + 32$

The method is exactly the same as solving a regular equation: use inverse operations to isolate the target variable.

$A = \frac{1}{2}bh$
$2A = bh$ multiply by 2
$h = \frac{2A}{b}$ divide by b

Solving for h in the area formula

Theory

Step-by-Step Method

To solve a literal equation for a variable:
1. Identify the variable you're solving for
2. Treat every other letter as if it were a number
3. Use inverse operations (same rules as always) to isolate your target
4. Check: the target variable should be alone on one side

Example 1

Solve $d = rt$ for $t$

We want $t$ alone. Currently $t$ is multiplied by $r$ .

Divide both sides by $r$ :

$t = \frac{d}{r}$

t = \frac{d}{r}

Example 2

Solve $y = mx + b$ for $x$

We want $x$ alone.

Step 1: Subtract $b$ from both sides:

$y - b = mx$

Step 2: Divide both sides by $m$ :

$x = \frac{y - b}{m}$

x = \frac{y - b}{m}

Example 3

Solve $P = 2l + 2w$ for $w$

We want $w$ alone.

Step 1: Subtract $2l$ from both sides:

$P - 2l = 2w$

Step 2: Divide both sides by $2$ :

$w = \frac{P - 2l}{2}$

w = \frac{P - 2l}{2}

Example 4

Solve $F = \frac{9}{5}C + 32$ for $C$

Step 1: Subtract $32$ :

$F - 32 = \frac{9}{5}C$

Step 2: Multiply by $\frac{5}{9}$ (the reciprocal):

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

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

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