Linear equations with one variable

A linear equation is one where the variable has a power of 1 — no squared ($x^2$) or cubed ($x^3$) terms are allowed.

In $x^2+3=12$, the variable is squared (power of 2). In $3x-5=10$, the variable $x$ has a power of 1. In $x^3=27$, the variable is cubed (power of 3).

$3x-5=10$ has the variable $x$ raised to the power of 1 only, making it a linear equation in one variable.

We need an equation where the variable appears with a power of 1 — no squared or cubed terms.

This has $x^2$, meaning the variable is raised to the power of 2. This is not linear — eliminate it.

$x^3=27$ has a power of 3, so it is not linear. $x^2-x=6$ contains $x^2$, so it is also not linear. Both are eliminated.

$3x-5=10$ is the only option where $x$ appears with a power of 1, making it the correct linear equation.

A variable is a letter that represents an unknown or changing value, such as $x$, $y$, or $n$.

$7$ is a constant (fixed number), $4$ is a constant, $31$ is a constant, and $n$ is a letter representing an unknown value.

The variable is $n$ because it is the letter representing the unknown value we are solving for.

A variable is a letter that stands for an unknown value. Constants are fixed numbers.

$7$, $4$, and $31$ are all fixed numbers — they are constants, not variables. Eliminate all three.

$n$ is the only letter in the equation, so it is the variable — the unknown we are trying to find.