AI Tutor
Every time your phone converts temperature from Fahrenheit to Celsius, it doesn't guess or run trial-and-error. It uses a rearranged version of the classic temperature formula that outputs Celsius directly.
A literal equation is an equation where variables represent most or all of the quantities, such as formulas in physics, geometry, and finance.
How do you rearrange an equation when you can't actually do arithmetic with numbers? Let's look at the golden rule.

The Golden Rule: Treat Other Variables Like Numbers

When isolating a target variable, apply the exact same inverse operations you use for standard numbers. The other letters simply come along for the ride.
Let's test this with the perimeter of a rectangle, P=2l+2wP = 2l + 2w, where we need to isolate the width ww.
First, subtract the term 2l2l from both sides to get P−2l=2wP - 2l = 2w. Then, divide the entire left side by 22 to obtain w=P−2l2w = \frac{P - 2l}{2}.
What happens when your target variable is locked inside a fraction or trapped inside parentheses?

Clearing Fractions and Unpacking Parentheses

To isolate a variable inside parentheses, either distribute first or clear the outer multiplier by dividing or multiplying by its reciprocal.
Consider the area of a trapezoid: A=12h(b1+b2)A = \frac{1}{2}h(b_1 + b_2). Let's isolate the base b1b_1.