Rearrange formulas and literal equations to isolate a specified variable (NC.M1.A-CED.4).

What this topic is asking

NC.M1.A-CED.4 asks you to solve a formula or literal equation for a specified variable, expressing it in terms of the others. A literal equation is one written with several letters (like $d = rt$ or $A = P + Prt$); rearranging it is the same algebra as solving a numeric equation, with the other letters treated as constants.

The core idea: letters are just constants

Rearranging a formula feels harder than solving with numbers, but it is the same process.

To solve $ax + b = c$ for $x$, you subtract $b$ and divide by $a$, getting $x = \frac{c - b}{a}$, exactly as you would if $a$, $b$, $c$ were numbers.

A rearranging routine

Clearing fractions and denominators

When the target sits in a fraction, multiply to clear the denominator first.

For $r = \dfrac{d}{t}$ solved for $t$: multiply both sides by $t$ to get $rt = d$, then divide by $r$ to get $t = \dfrac{d}{r}$. Clearing the denominator before isolating avoids working with a variable in the bottom.

How the NC Math 1 EOC examines this topic

• Multiple choice. Choose the correctly rearranged formula.
• Gridded response. Rearrange a formula, then substitute values and enter the result.
• Calculator-active. Often a two-step item: solve for the variable, then compute.

Literal equations connect directly to solving linear equations, where letter coefficients first appear, and to creating equations, since a model is often more useful after being rearranged for the quantity you want.

Why one formula answers many questions

The value of rearranging is efficiency. The single relationship $d = rt$ can be read three ways: $d = rt$ to find distance, $t = \frac{d}{r}$ to find time, and $r = \frac{d}{t}$ to find rate. Rather than memorizing three formulas, you keep one and rearrange as needed. This is also why A-CED.4 is tested: a student who can rearrange does not need a formula sheet for every variant, which matters on NC Math 1 where no reference sheet is provided. Mastering rearrangement turns each formula into a flexible tool instead of a fixed recipe.

A worked formula with the target in two places

Sometimes the target appears more than once, and you factor it out.

Factoring out the target is the move whenever it occurs in multiple terms; you cannot isolate it by subtraction alone.

Try this

Q1. Solve $C = 2\pi r$ for $r$. [1 point]

• Cue. Divide by $2\pi$: $r = \dfrac{C}{2\pi}$.

Q2. Solve $I = Prt$ for $r$. [2 points]

• Cue. Divide both sides by $Pt$: $r = \dfrac{I}{Pt}$.