6-3 One-Step Subtraction Equations

Property

To model a situation where a quantity is decreased, we can use a subtraction equation of the form $x - a = b$. Here, $x$ represents the initial amount (the unknown), $a$ is the amount being taken away, and $b$ is the final amount remaining.

Examples

• After giving away 8 pencils, Maria had 15 pencils left. To find how many pencils she started with, $p$, we can write the equation: $p - 8 = 15$.
• A baker had a full bag of flour. After using $2.5$ kilograms for a batch of bread, he had $1.75$ kilograms of flour left. To find the initial weight of the flour, $w$, we can write the equation: $w - 2.5 = 1.75$.

Explanation

Many real-world problems involve a starting amount, a change, and a resulting amount. When an amount is removed or decreased, you can represent the situation with a subtraction equation. First, identify the unknown quantity and assign it a variable, then write the equation that shows the starting amount minus the amount taken away equals the final amount.

Property

Addition and subtraction are inverse operations, which means they undo each other. To undo the subtraction of a number, you add the same number.