Chapter 2
Linear Equations
You bought five identical notebooks and one three dollar pen, and the receipt says thirteen dollars in total. What did each notebook cost? You could guess a price, add it up, and guess again, but guessing is slow and it never proves that no other price fits. So far algebra has been about writing expressions that describe a situation. An equation does something else. It says that two amounts are equal and leaves one of them unknown, and pinning that unknown down never has to be a matter of luck.
What You'll Explore
4 lessons.
- Solving Linear Equations
Nobody solves an equation by staring at it; they change it into an easier one, over and over, until the answer is obvious. But changing an equation is only fair if the new one has the same solutions as the old. Which changes are fair is the question this lesson settles.
- Linear Equations in Disguise
Some equations arrive buried under fractions, decimals, or a variable in a denominator, and none of them look like the tidy ones from the lesson before. Underneath, most of them are. You will also meet an equation whose variable vanishes as you simplify, which raises a question about how many solutions an equation can have.
- Word Problems with Linear Equations
Word problems hide their algebra in sentences: a rope cut into two pieces, a sister twice your age in five years, a price after a discount. Solving the equation is the easy half. The harder question is how a paragraph turns into one equation, and which quantity you should name to get there.
- Solving for a Variable
The area of a rectangle is its length times its width. If you already know the area and the length, you would rather have a formula that hands you the width directly. This lesson asks what changes about solving when the quantities you are working around are letters instead of numbers.