AI Tutor
If a submarine at an altitude of −150-150 meters rises at 4.54.5 meters per minute, where will it be after 1212 minutes?
An algebraic formula gives you the exact blueprint, but to find the real answer, you need to plug in numbers and simplify step-by-step.

The Substitution Rule

A rational number is any number you can write as a fraction of two integers, including whole numbers, negative numbers, fractions, and terminating or repeating decimals.
When you evaluate an expression, you replace each variable with a given value and simplify using the order of operations.
Always place parentheses around the value you plug in. These parentheses protect negative signs and fractions from accidentally changing operations.
What happens when an expression contains exponents alongside negative inputs? Let's look at why parentheses matter so much.

Exponents and Negative Inputs

Let's evaluate 3x2−5x3x^2 - 5x when x=−2x = -2.
First, substitute (−2)(-2) in place of every xx: 3(−2)2−5(−2)3(-2)^2 - 5(-2)
Notice that (−2)2=+4(-2)^2 = +4 because the negative sign is inside the parentheses being squared. Without parentheses, −22-2^2 means −(22)=−4-(2^2) = -4, which would lead to an incorrect answer.