6-2 One-Step Addition Equations

Property

To model a situation where a quantity is added to an unknown value to get a total, we use an equation of the form $x + a = b$. Here, $x$ represents the unknown starting amount, $a$ is the amount added, and $b$ is the final total.

Examples

• After receiving 8 new text messages, your phone shows you have 25 total messages. To find the original number of messages, $m$, you can write the equation: $m + 8 = 25$.
• You add 1.5 gallons of gasoline to your car, which brings the total amount of gas in the tank to 7.8 gallons. To find the amount of gas you started with, $g$, you can write the equation: $g + 1.5 = 7.8$.

Explanation

Translating real-world problems into equations helps us solve them systematically. First, identify the unknown quantity and assign it a variable, like $x$. Then, look for keywords like "plus," "added to," "increased by," or "sum" that indicate addition. The final step is to set up the equation by showing how the initial amount, the change, and the total are related.

Property

Inverse operations are mathematical operations that reverse, or "undo," the effect of each other. Subtraction is the inverse operation of addition.

To undo the addition of a number, you subtract that exact same number: