Subtraction Property of Inequality

Property For any real numbers $a$, $b$, and $c$: If $a < b$, then $a c < b c$. If $a b$, then $a c b c$. If $a \leq b$, then $a c \leq b c$. If $a \geq b$, then $a c \geq b c$. Explanation Just like adding, subtracting the same amount from both sides of our trusty inequality seesaw keeps it balanced in the same way. This lets you clear out extra numbers that are added to your variable, getting you one step closer to solving the puzzle. It’s the perfect partner to the addition property, helping you isolate that sneaky variable! Examples To solve $x + 7 10$, you subtract 7 from both sides: $x + 7 7 10 7$, which gives you the solution $x 3$. For an inequality with decimals like $k + 3.3 \leq 5.5$, you do the same: $k + 3.3 3.3 \leq 5.5 3.3$, which simplifies to $k \leq 2.2$. If your allowance plus 5 dollars is at least 15 dollars ($a+5 \geq 15$), solve by subtracting 5: $a \geq 10$ dollars.