Algebra

Linear Equations


In the last chapter, we covered the parts of an equation. Now, let’s talk about a certain type of an equation: the Linear Equation. A linear equation is an equation that consists of a variable multiplied by a number, added to a constant. For example, \(12x-5=0\) is a linear equation. So is \(58x+119=0\). In general, a linear equation can be written as:

\[ax+b = 0\]

where \(a\) and \(b\) are constants and and \(x\) is a variable. Note that you will often see \(x\) as a variable.

In a linear equation, \(a\) is a coefficient. A coefficient is the number next to a variable - the coefficient is always multiplied by the variable. The coefficient is negative if the term is being subtracted.



Questions (3)

Is \(7x^2-x+3=0\) a linear equation?

[Show answer]
No, because there is a term with \(x^2\).

Is \(3x+4=9\) a linear equation?

[Show answer]
Yes, because there if we subtract \(9\) from both sides, we see that it can be written as \(3x-5=0\).

In the linear equation of \(12x+5=0\), what is the coefficient for the \(x\) term?

[Show answer]
\(12\), because that is the number being multiplied by \(x\).

Terms (2)

Linear Equation

An equation that can be written in the form \(ax+b=0\), where \(a\) and \(b\) are constants,

Coefficient

The number next to a variable. The variable is multiplied by the coefficient.