SAT Math 1: Linear Equations in One Variable

Linear equation

An equation that can be written as $a_1x_1+a_2x_2+\cdots+a_nx_n+b=0$, where the variables appear only to the first power and are not multiplied by one another. The coefficients are constants, and at least one variable coefficient must be nonzero.

What makes a solution satisfy a linear equation?

A solution is a value or tuple of values that makes the equation true when substituted for the variables.

How is a linear equation in one variable written and solved?

It can be written as $ax+b=0$ with $a\ne0$. Its unique solution is $x=-\frac{b}{a}$.

What happens if all variable coefficients in a one-variable equation are zero?

The equation becomes $b=0$. If $b=0$, every value of the variable is a solution; if $b\ne0$, the equation has no solution.