Literal Equations and Formula Rearranging
Practice isolating one variable in terms of others, a frequent PSAT algebra task.
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Questions Covered in This Set
10 cards to master
What is a literal equation?
An equation with several letters where you isolate one variable; the answer is an expression, not a number.
What does the phrase "in terms of" signal?
Get the named variable alone on one side, with all other letters on the other side.
Solve F = (9/5)C + 32 for C
C = (5/9)(F − 32) — subtract 32, then multiply by the reciprocal 5/9.
Solve ax + b = cx + d for x
x = (d − b)/(a − c): collect x terms, factor out x, then divide by (a − c).
What do you do when the target variable appears twice?
Collect those terms on one side and FACTOR the variable out, then divide by the whole parenthesis.
What if the variable you want is in a denominator?
Multiply both sides by that variable first to free it, then continue solving.
Solve V = πr²h for r
r² = V/(πh), so r = √(V/(πh)) — keep only the positive root for lengths.
Describe the plug-in-numbers strategy
Pick friendly values for the variables, compute the result, then test each answer choice to see which gives the right output.
Solve S = 2πr² + 2πrh for h
h = (S − 2πr²)/(2πr)
Name three common mistakes in literal equations
Dropping parentheses, dividing only part of a side, and forgetting to factor when the variable appears twice.
